Genesis 17:10 - Matthew Poole's English Annotations on the Holy Bible

Circumcision is here called the covenant by a usual metonomy, because it is the condition, sign, and seal of the covenant, the pledge of God's promise and man's duty. And upon the same grounds the cup, i.e. the wine, is called the new testament in Christ's blood, Luke 22:20; or, which is all one, Christ's blood in the new testament, Matthew 26:28. It is evident that women as well as men were comprehended in this covenant, from Genesis 34:14 Exodus 12:3,4 Joe 2:15,16. Yet circumcision is given only to the males, partly, because it could not, at least not conveniently, be administered to females; partly, because man is the principal cause of the propagation of children, and consequently of the propagation of that original corruption which cleaves to them; partly, to signify that all persons begotten by man should be polluted by sin, though not all conceived by a woman, as Christ was; and partly, because man is the head of the woman, and of the family, upon whom all their concerns are devolved, and from whom the distinction of families and people comes.