That would be the question if the Bible was neutral on the subject. However, the Bible seems to lean in favor of including children as demonstrated in some of the posts above. Never does the Bible teach that there are some who should be excluded from the preached word.
Neh 8:1 says that "all the people gathered themselves together as one man" to hear Ezra preach. Then in 8:2 it says that "Ezra the priest brought the law before the congregation both of men and women, and all that could hear with understanding..."
I believe Ezra preached the law to "all the people". But of course, those who could not understand because of their age or their mental capacity did not 'hear' (shama) or 'hearken'. But if a special 'children's church' had been set up then the people who were 'babysitting' would not hear Ezra's preaching.
Once again, where did you come up with the age of '10'? To quote Kramer, "It seems capricious and arbitrary." Who gets to decide when a child can understand? When they make a credible profession of faith?
Look, if you want to argue that children's church is sometimes necessary, then fine, use your 'brotherly love' verses, but you cannot go so far as to say that it
must be so. The Bible teaches that children are a blessing from the Lord and I could just as easily argue that to remove my children from the worship service would be 'unloving' to my brother.
Of course the preacher does have the responsibilty of including some bread of life for the children in the service as well. And what happens in my church (I can't speak to every church) is that those parts of the message that I make clear enough for children are the parts that the sheep as a whole remember most! In fact, Christ said we are to come to Him as babes! Maybe we can learn something from these children in our midst.
Once again, I am trying to bind anyone's conscience. If you pastors are compelled to establish a nursery or children's church then do so. But that does not make it the rule for every church.