John Chrysostom
The rite of circumcision was first delivered to Abraham as a sign of distinction, that the race of the Patriarch might be preserved in unmixed purity, and so might be able to obtain the promises. But now that the promise of the covenant is fulfilled, the sign attached to it is removed. So then through Christ circumcision ceased, and baptism came in its place; but first it was right that John should be circumcised; as it is said, And it came to pass, that on the eighth day, &c. For the Lord had said, Let the child of eight days be circumcised among you. (Gen. 17:13.) But this measurement of time I conceive was ordered by Divine mercy for two reasons. First, because in its most tender years the child the more easily bears the cutting of the flesh.
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Secondly, that from the very operation itself we might be reminded that it was done for a sign; for the young child scarcely distinguishes any of the things that are around him. But after the circumcision, the name was conferred, as it follows, And they called him. But this was done because we must first receive the seal of the Lord, then the name of man. Or, because no man except he first cast aside his fleshly lusts, which circumcision signifies, is worthy to have his name written in the book of life.
But the name John is also interpreted the grace of God. Because then by the favour of Divine grace, not by nature, Elisabeth conceived this son, they engraved the memory of the benefit on the name of the child.