Paedobaptism

After the baptism talk we had at our last gathering, I've heard more and more stuff relating to baptism. I haven't gone out of my way very much to read things about it since the topic really doesn't have much bearing on my life right now, but I still have some questions about paedobaptism that I'm hoping some of you who understand it can answer.

The other day in a class at WTS, a professor made a side comment where he said he had a hard time with Presbyterians' view on paedobaptism because it's supposedly welcoming the infant into the covenant family and yet the child cannot come to the family table (communion) until he becomes a member of the church. I had never realized that that was the case in Presbyterian churches. In the Methodist church I grew up in we were always allowed to take communion even before we went through confirmation and joined, and in the Anglican church I went to in Columbia children were allowed to take communion if they were with their parents.

So what's the deal? How can we call what we're doing baptism if it doesn't result in the child having the benefits (I would say communion is one of the most important benefits) of being a member of the covenant family. I'm sure that this incongruity hasn't gone unanswered by Presbyterians, so does anyone know the answer?

Looking forward to hearing from y'all. And also, where are these updates I've been asking for for the last month or two? I want to hear how y'all are doing.