So, what I think is missing from most discussions and debates between paedobaptists and credobaptists, is a thorough explanation of the structure of covenants throughout redemptive history, specifically focused on the nature of the covenant of grace as expressed to Abraham.
All Biblical covenants have signs pointing to aspects/conditions of the covenant and seals, marks of agreement or inclusion in the covenant. Covenants are sealed with initiation rites, bloody ceremonies expressing conditions and penalties of the covenant. The signs have both positive and negative implications.
With Abraham and God, God takes on himself the first sign, walking between the pieces of the slain animals. In this God is saying negatively: ‘If I fail to keep my promises to you, may I be cut in two like these animals.’ and positively: ‘I will provide a sacrifice for you.’ Abraham takes on the sign of circumcision, and in this he is saying (and likewise all his offspring), positively “As the foreskin is separated, so shall God separate me from my sin.” and negatively, “As the foreskin is separated from my body, so shall I be from God’s people if I fail to trust in him.”
Baptism thus carries a similar symbolism, it is not merely the sign of our burial in Christ, but God’s solemn promise to ‘remove sin from our body as water washes away dirt.’ It is in effect, analog to circumcision without the blood, and points to the once-for-all blood shed on the cross. But circumcision also has a negative implication, it is a sign not only of salvation, but of wrath.
For Noah and his family, the flood was actually salvation from sin, but for the unbelieving world, it was God’s wrath. Baptism thus also serves this negative sign, it promises wrath to those who partake of the covenant sign, and fail to fulfill the covenant conditions. (As Calvin 1, Turretin 2, Hodge 3, etc explain.)
It is with this understanding that the warning passages in Hebrews take on true significance. These are not hypotheticals, they’re not pointing to a true ‘loss of salvation’, both of which ignore the covenantal foundation of the book. Rather, the warning passages promise a cutting off of people from the covenant people of God for one thing, a failure to believe.
This also makes sense of the difficult passages in 1 Peter and explains why the flood is tied to baptism. This coventantal continuity and acceptance of the overarching themes and structures established by God himself throughout redemptive history is what caused me to become a paedobaptist. I could not, with good conscience, continue to hold that the New Covenant was such a departure from God’s established method of covenant establishment, without express warrant by the Apostles.
In fact, I believe the opposite is seen in their writings. Rather than the suggestion that only those who have the mental and physical ability to mouth certain words should be given the means of grace, we see that God’s promise is truly to “you and for your children and for all who are far off, everyone whom the Lord our God calls”. This covenantal language expresses the very same structure as that provided to Abraham. The promise is to your and your children (faithful Jews), and to people beyond your race (faithful Gentiles).
Thus Baptism is a sign of God’s promise, that depends on a condition, that condition is faith, if one fails to believe (either the adult convert or the infant community member), the flood of God’s wrath is promised.