Matthew Poole and continuators on Genesis 17:10

10 This is my covenant which ye shall keep between me and you, and thy Seed after thee: every man-child among you shall be circumcised.

Circumcision is here called the Covenant by an usual Metonymy, because it is the condition, sign and seal, of the Covenant, the pledge of Gods promise and mans duty. And upon the same grounds the cup i. e. the Wine, is called the New Testament in Christs blood, Luke 22. 20. Or, which is all one, Christs Blood in the New Testament, Matth. 26. 28.

It is evident that Women as well as Men were comprehended in this Covenant, from Gen. 34. 14. Exod. 12. 3, 4. Ioel 2. 15, 16. Yet Circumcision is given only to the Males, partly because it could not, at least not conveniently, be administred 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 signifie 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.

Marginal references: Acts 7. 8.