Let's think this through.
1) Reformed theology taught creationism. Lutherans taught
Traducianism.
2) Tertullian seems to be the author of Traducianism.
3) The most common opinion of this (because there are more than one), think the soul is propagated by the soul, not by a decision and partition of the paternal soul, but in a spiritual manner.
4) Turretin says the Reformed hold to creationism for three reasons: (1) from the law of creation; (2) from the testimony of Scripture; (3) from reasons.
Here is how Turretin deals with the three:
From the law of creation, because the origin of our souls ought to be the same as of the soul of Adam; not only because we ought to bear his image (1 Cor. 15:47, 48), but also because his creation (as the first individual of the whole species) is an example of the formation of all men (as the wedlock of our first parents was an example for the rest). But the soul of Adam was created immediately by God, since "he breathed into his nostrils the breath of life" (Gen. 2:7). Thus it is evident his soul was not produced from potent material, but came to him extrinsically through creation and was infused into the body by the breath of God himself. Nor ought it to be objected that we cannot argue from Adam to ourselves because the same thing might be said of the origin of the body (which nevertheless is not the case, since ours is generated from seed, while that of Adam was created from the dust of the earth). Although there may be a disparity by reason of the efficient cause on account of the diversity of the subjects (because as the body is elementary and material, it can be produced by man through generation; but the soul, being immaterial and simple, cannot spring from any other source than God by creation), yet with respect to the material cause a comparison may rightly be made. For as the soul of Adam was created out of nothing, so also are the souls of his posterity; and as his body was formed of the dust of the earth, so also our bodies from seed (which itself also is earthly and material). Therefore the mode of action with respect to Adam was also singular, yet the nature of the thing is the same in both cases. This is confirmed by the production of Eve herself whose origin as to the body is described as from a rib of Adam, but of the soul no mention is made. Hence it is plainly gathered that the origin of her soul was not different from that of the soul of Adam because otherwise Moses would not have passed it over in silence (his purpose being to describe the origin of all things). And Adam himself would have mentioned this origin, yea he would have declared it specially; he would have said not only "this is bone of my bones," but "soul of my soul" (Gen. 2-23). This would have set forth more strongly the bond of wedlock, which should be not only in the bodies, but also in the souls. Finally, if Adam's soul and ours had a different origin, they could not be said to be of the same species because his was from nothing. Ours, however, would be from some preexisting material wholly dissimilar.
Second Argument:
Second, from the testimony of Scripture, in which God is spoken of as the author and Creator of the soul in a peculiar manner distinct from the body: "œThen shall the dust return to the earth as it was: and the spirit shall return unto God who gave it." (Ecc. 12:7). Here a manifest difference is marked between the origin and the destruction of the body and the soul. The one is said to return to the dust (whence it was taken); the other, however, to return unto God (who gave it). Therefore since the body returns thither whence it had its origin, so also the soul. This is more clearly confirmed by the fact that God is said to "give the spirit" (which cannot be understood of the common giving by concourse with second causes). For he also gives the body itself no less than the soul because he is the first cause of both (nor would he well be said by antithesis [kat'antithesin] to have given the spirit). Rather this is understood concerning the proper and peculiar mode of origin (which does not belong to the body). Nor ought it to be said that this is to be referred to the first creation of Adam. The scope, the words and circumstances of the text prove that it treats of the ordinary birth and destruction of men. Accordingly their bodies return to the dust (i.e., to the earth) whence they were taken, while their spirits return unto God, the judge, who gave them (either for glory or for punishment).
V. "The word of the Lord, which stretcheth forth the heavens, and layeth the foundation of the earth, and formeth the spirit of man within him" (Zech. 12:1). Whence a multiple argument is drawn for the creation against the birth of the soul (psychogonian). (1) He is said to form the spirit of man within him; therefore he ought to produce it immediately without the intervention of man. (2) The formation of the spirit is joined with the stretching out of the heavens and the founding of the earth, as of the same order and grade. Therefore since the former two are works of omnipotence, made immediately by God and without second causes, so the last ought to be also. Nor can this be referred to the mediate production of God because thus man would be admitted to a participation of causality, which the text does not allow (since it asserts the production of the soul as well as that of the heaven and earth to be peculiar to God). However, this is falsely restricted to the first production of man since it ought to be extended equally to all. Hence when it speaks of the production of the soul elsewhere, the Scripture does not use the singular (as if referring to the one soul of Adam), but the plural (Ps. 33:15; Is. 57:16). But man here is not taken individually for Adam, but specifically for any man.
VI. "We have had fathers of our flesh which corrected us, and we gave them reverence:shall we not much rather be in subjection unto the Father of spirits, and live?" (Heb. 12:9). And Peter calls him in a peculiar manner a "faithful Creator of souls" (I Pet. 4:19). In Num. 16:22, God is called 'the God of the spirits of all flesh.' So too Is. 57:16: "For I will not contend forever, neither will I be always wroth: for the spirit should fail before me, and the souls which I have made.' Now why should God be called "the Father of spirits" in contradistinction to "the fathers of the flesh" unless the origin of each was different? And yet if souls are propagated, the parents of the body and the soul should be the same. Indeed "the flesh" here cannot signify the old man or inborn corruption because then it would not be opposed to spirits (pneuniasi) in the plural, but to spirit (pneumati) in the singular. Rather it designates the body, and they are called 'fathers of the flesh" who generate the flesh. So the word "spirit" ought not to be referred to spiritual gifts (which are not treated of here), but to the other part of man opposed to the body. Nor can the omission of the pronoun hamon (with respect to the flesh) be a hindrance because it is to be repeated apo koinou (since he speaks about the same according to the principles and origin of the diverse parts). Hence in Num. 16:22, he is called "the father of the spirits of all flesh" (i.e., of all men). Again he cannot be called "the Father of spirits" mediately, as he is called "the father of the rain" (job 38:28) because he is its author (although not immediately). Thus the antithesis between the fathers of the flesh and the father of spirits would not stand, and the force of the apostolic exhortation to afford greater obedience to God than to earthly fathers would fall. Nor if the concourse of God is not excluded from the production of the flesh (although attributed to earthly fathers because he is the universal first cause), ought the concourse of man in the production of the spirit to be excluded (because he is the particular second cause).
Third Argument:
Third, the same thing is proved by arguments from reason. The soul is propagated by generation, either from both parents or from one only; either as to its totality or only as to a part. But neither can be said. Not the former because thus two souls would coalesce into one and be mingled. Not the latter, for if from one (either the father or the mother only) no reason can be given why it should be propagated by the one rather than by the other (since both parents are equally the principle of generation). If the whole is propagated, then the parents will be without it and so will be deprived of life. If a part, it will be divisible and consequently material and mortal. Nor can it be reasonably replied here that neither the whole soul nor a part of it is propagated, but a certain substance born of the soul and (as it were) an immortal seed of the soul. For it is taken for granted that there is a seed of the soul by which it either generates or is generated; yet such a seed cannot be granted (which does not fall from the soul), and therefore proves it to be material and divisible.
VIII. Again, all modes of propagation are pressed by the most serious difficulties; nor can they be admitted without overthrowing the spirituality of the rational soul. Not the first, which is held by those who consider the soul to be produced from the power of seed so that it is begotten with the body. For the effect cannot (in the total genus) be more noble than its cause; nor can things corporeal and elementary be so elevated as to produce a spiritual and rational thing. If generated from seed, with the seed also it will be corrupted. Men and brutes would have the same origin and consequently the same destruction. Not the second, which is held by those who think the soul of the son to be from that of the father in a manner inscrutable and unknown by us. This entangles rather than unfolds the matter. For the father produces the son either from some preexistent matter or from none; not from none because he would thus create; not from some because either it would be the corporeal substance of a seed (which has just been proved to be false) or it would be a certain spiritual substance of the soul (which again cannot be said). This is true because that spiritual substance is made either from the whole soul of the father or from a part only. Not from the whole because thus the soul of the father would vanish and be converted into that spiritual seed. Not from a part because thus the soul of the father would be divisible into parts, and because that substance is corruptible and perishes in the very instant the soul is produced. But then it will no longer be a spiritual or incorruptible substance. Thus it would follow that there are two spirits in the begotten man: the soul of the son and the spiritual substance from which his soul was produced. Besides, it is repugnant to the nature of seed for it to remain after the generation of the thing (because it ought to be transmuted into what springs from the seed).
IX. Not the third even though it may seem preferable to others. They hold that it is said to be propagated not by alienation, but by communication (as when light is kindled from light without any division of the other). (1) But the communication made of one and the same thing and without any alienation occurs only in an infinite and not in a finite essence (in which the same numerical essence cannot be communicated to another, but a similar only is produced). (2) The soul of the son cannot be produced from that of the father; neither terminatively (because the terminus a quo perishes, the terminus ad quem being produced), nor decisively (because the soul is without parts [ameristos]), nor constitutively (because the soul of the father is not a constitutive part of the soul of the son). (3) The similitude of the light does not apply. Besides the fact that the flame and candle are corporeal substances (while here the subject is a spiritual), it is certain that light is produced from the potency of the material. Nor can it be kindled without a decision of fiery particles transmitted from the lighted to the extinguished torch (which cannot be said of the soul).
X. Since, therefore, the opinion of propagation labors under inextricable difficulties, and no reason drawn from any other source forces us to admit it, we deservedly embrace the option of creation as more consistent with Scripture and right reason. This was also evidently the opinion of most of the heathen philosophers themselves. Hence the following expression of Zoroaster according to Ficinum: "You must hasten to the sunlight and to the father's sunbeams: thence a soul will be sent to you fully enslaved to mind" (Chre speudein se pros to phaos, kai pros patros augas Enthen epemphthe soi psyche! polyn hessamenif noun, Theologia Platonica de immortalitate animorum 10 [1559], p. 160). Aristotle asserts that "the mind or intellect, and that alone enters from without, and is alone divine" (ton noun thyrathen epeisienai kai theion einai monon, Generation of Animals 2.3.27-28 [Loeb, 170-711). Cicero says, "No origin of the soul can be found upon earth for there is nothing in the soul mixed and concrete that seems to be or born from the earth and made.... Thus whatever that is which perceives, knows, wishes and flourishes, is heavenly and divine and on that account must necessarily be eternal" (Tusculan Disputations 1.66 [Loeb, 76-791).
XI. God is said to have rested from all his work (Gen. 2:2), not by retiring from the administration of things, but by ceasing from the creation of new species or individuals (which might be the principles of new species). Thus he works even now (Jn. 5:17) by administering the instituted nature and multiplying whatever was; not, however, by instituting what was not. Now the souls which he creates every day are new individuals of species already created.
XII. Although the soul is not propagated, the divine blessing given at first (Gen. 1:28) does not cease to exert its power in the generation of men. For God always cooperates with the generators and the generation, not only by preserving man's prolific power, but also by infusing the soul into the disposed body.
XIII. It is not necessary in order that man may be said to generate man that he should generate all natures or essential parts of the compound. Otherwise, the blessed virgin did not beget true God and man. Rather it suffices that he prepares and works up the material and renders it fit for the introduction of form and attains the union of the soul with the body (by which man is constituted in his being as man and is made such a physical compound). For generation tends to the compound, not however to the production of both parts. As man is said to kill a man (who dissolves the union of the soul with the body although he does not even touch the soul), so man generates man because he joins together those parts from which man springs although not a soul-begetter (psychogonos). Nor ought he who generates the whole man to be forthwith the producer of the whole of man.
XIV. Adam can be said to have begotten man after his own image, although he did not produce the soul. The cause of the similitude is not the propagation of the soul, but the production of bodies of the same temperament with the parents. For from the different temperament and humors of the body, different propensities and affections are also born in our souls.
XV. When souls are said to have "gone out of the loins of Jacob" (Gen. 46:26), they are not understood properly, but synecdochically for the "persons" (a most usual manner of expression with the Scriptures). Moreover, there was no need that Jacob should contribute anything to the production of these souls. It suffices that he concurred to their conjunction or subsistence in the body mediately or immediately. Therefore they are said to have gone out, not as to being or substance simply, but as to subsistence in the body and union with it.
XVI. Although Christ was no less in Abraham (according to the flesh) than Levi (who was tithed in his loins, Heb. 7:9-10*), it does not follow that Levi was in him according to his soul (so that the soul of Levi was propagated and that a distinction may be preserved). Rather Levi (with respect to person) was in Abraham according to seminal mode and the natural powers of the father and mother (from whom he was to be bom). But Christ was in him only as to the human nature with regard to the mother; not, however, as to his divine nature and person. Thus his person could not be tithed; but as a superior he tithed Abraham and blessed him in Melchizedek (his type), not as man, but as the Mediator, God-man (theanthropos), performing a kingly and priestly office.
XVII. The propagation of original sin ought not to cause a denial of the creation of souls and the adoption of propagation because it can be sufficiently saved without this hypothesis (as will be demonstrated in its place). Although the soul is not materially from Adam (as to substance), yet it is originally from him as to subsistence. And as man is rightly said to beget man (although he does not beget the soul), so an impure progenerates an impure, especially (the just judgment of God intervening) that by which it was established that what he had bestowed upon the first man, he should at the same time have and lose for himself as well as his posterity. Now although it is curious to inquire and rash to define why God infuses a soul tainted with sin and joins it to an impure body, it is certainly evident that God did not will (on account of the sin of man) to abolish the first sanction concerning the propagation of the human race by generation. Thus the order of the universe and the conservation of human nature demanded it.
I think he does a good job with this.
