Adam Clarke on Leviticus 12:3

And in the eighth day - Before this time the child could scarcely be considered as having strength sufficient to bear the operation; after this time it was not necessary to delay it, as the child was not considered to be in covenant with God, and consequently not under the especial protection of the Divine providence and grace, till this rite had been performed. On circumcision see Clarke's note on Gen 17:10. Circumcision was to every man a constant, evident sign of the covenant into which he had entered with God, and of the moral obligations under which he was thereby laid. It was also a means of purity, and was especially necessary among a people naturally incontinent, and in a climate not peculiarly favorable to chastity. This is a light in which this subject should ever be viewed, and in which we see the reasonableness, propriety, expediency, and moral tendency of the ceremony.