Calvin here shows the usual paedobaptist misunderstanding of types, shadows, and symbols. Abraham and his immediate physical seed, circumcised by virtue of being physically born, were painting a picture of a people, the sons of Abraham in a way that really matters, entering the New Covenant community by means of the New Birth. Like the other types and shadows of the OT, circumcision fades in the glory of what it was merely shadow of.
His only argument--and the most common one--is: "children were not denied covenant membership them, so why deny it now?" Well, because physical descent has nothing to do with salvation now: "Think not to say to yourselves, 'we have Abraham for our father'". In this New Covenant, founded on better promises, all the nations of the earth are commanded to be born again, and thus are born into the family of God. Having been joined to the Seed of Abraham by this new birth, they receive the sign of an unbreakable covenant: of the real fulfilment of the covenant that God made with Abraham.