Family membership and infant baptism

Steve Hays posts what he calls a "modest little argument for infant baptism".

Infant baptism, he says, is justified by the recognition that you are born into a church community. But infant communion is not thereby justified.

1. The division is arbitrary. What kind of community calls you a member but does not allow you to take part in the community meals?
2. Baptism means what Jesus says it means, and that is that is that it is a sign of discipleship/New Covenant membership. We're not free to play around with the definition, and make it a social ordinance as Hays proposes.
   
3. The Bible teaches that initiation into the New Covenant is via the new birth. Hays, as all covenantal paedobaptists, is right to say that it's about family membership, and that it should be for all those born into the family. But the question is, which family - and how are we born into it? Hays and those like-minded, in this issue, are still camped out with Nicodemus.