One discrepancy that I began to see before I became a Baptist: I was apparently included in the Christian church (family) by baptism, but not entitled to the family meal, despite the OT evidence of family participation. And this on the basis of one NT text!
This quote by Guy Waters underscores the point: “The fact that the Supper is a family meal reinforces a distinction between the church and those who are not part of the church.” So, was I part of the church as a baptized infant or not? Was I part of the family or not?
This places children in a confusing place—belonging but not really belonging. And what I began to see is that if Jesus only invites disciples to the Lord’s Supper, the same must also be true of baptism.