Christians' children are worse off if not baptised during infancy?

"Those who claim that Hebrew infants should be circumcised, but that ours should not be baptized, make God more gracious to Jews than to Christians." - Peter Martyr Vermigli (Commentary on Romans, chapter 4 verse 11)

This is, of course, an archetypal supporting argument within circles that teach infant baptism for children of believers. And on the surface, it has an immediate plausibility: if Jews' children received the sign of welcome into the covenant family, then why would Christians' children no longer possess that sign? Has this privilege been withdrawn from them?

It is, however, not truly an argument at all. It is not an argument, but a re-wording of the conclusion. It is a statement that only follows if the actual argument has already been accepted. If the actual argument has not already been accepted, it does precisely nothing to advance it.

How so? Lying behind the statement is the belief that circumcision and baptism are not only divine ordinances with similarities as well as differences, but are fundamentally and essentially the same thing. Any differences are of strictly limited import and finally of no real weight in any practical matter, for they are both "the outward sign of the covenant of grace", signifying and sealing the recipient's membership of that covenant.

And note there that another concept has been admitted which must be viewed in a certain way, in order for that equation to work: there must be a "covenant of grace", and this covenant of grace cannot merely be a unifying concept for understanding God's overall plans throughout salvation history. It is absolutely required that all actual historical covenants (or, at least all those after the fall) found in the Bible, again, despite all their differences, are in the end found to be essentially the same thing, and these differences all found to be of no final weight or import. All Biblical covenants in history do not simply flow from, reflect or advance the purposes of the covenant of grace.... rather, they are "administrations" of this covenant of grace. Note specifically that what cannot be the case is that the New Covenant is the one actualisation in history of an eternal covenant, i.e. the New Covenant is "the covenant of grace" with all the preceding covenants being entities that should be approached firstly upon their own terms, whilst still being intended to ultimately reveal, lead to, and having a deeply important underlying continuity with it. That position (i.e. the Reformed Baptist position) is not enough; all covenants must fundamentally be the covenant of grace. There is really, in practice, only one covenant, under different names and times. The signs and outward accompaniments may change, but the covenant is always one and the same. Jews and Christians must, at the root of it, be the same thing: members of the one-and-only salvific covenant. Again I repeat: we are not talking here about underlying unity, but of to-all-intents-and-purposes identity.

Only then, if all this is accepted, can you speak as Peter Martyr does. Only then can we say that the immediate offspring of a descendant of Abraham according to the flesh before the coming of Christ has received "more grace" than an infant born to believing Christian parents, if the former (assuming that it's a male child) is circumcised on the eighth day, whilst the latter is not sprinkled with sacramental water. But as I say: that's actually the thing to be proved. In and of itself, "but then that means God has been less gracious to Christians than he has been to Old Testament Jews!" is not any sort of argument. It is merely the re-statement of the thing to be proved, but using different words. And as such, in all honesty, it ought to be struck out of the canons of paedobaptist argumentation. It has no actual content that is specific to itself. It simply re-labels the other, real arguments. It is not a supporting sub-argument: it is merely the begging of the question.