The distinction and concession underscores the reality that Salvation is always by Grace and not Race while at the same time maintaining that because of Grace, Grace often runs in familial lines (Deuteronomy 7:9).
And so we believe with Scripture that whenever God made covenant with man He always included the children of whom He made covenant with in that covenantal arrangement.A Short Rationale for Infant Baptism by Pastor Bret McAtee of Iron Ink
"The father says, in effect, by keeping him at arm's length from any covenant blessings, that his profession of faith and trust is more worthy of doubt than credence, and this is the first (twisted) covenantal lesson the child learns. Christian parents are commanded to teach their children to believe, and instead, in the name of high conversion standards, we teach them to doubt. Then, when they grow up and mature in the doubting that we have taught them, we point to that doubt as clear evidence that we did the right thing in keeping them away in the first place" (A Primer on Worship and Reformation, p. 73).from Pastor Douglas Wilson of Blog and Mablog