We know about circumcision from Avraham’s circumcising his two sons. Also from the failure of Moses to circumcise his son that nearly caused his death. But here we have the actual law stated as part of the constitution, rather than through a narrative.
Why is circumcision such fundamental law and why is there no female equivalent in Judaism? Once again one might say it is a chok. A non-rational expression of one’s commitment to God and to the people. It symbolizes the partnership between God, parents and the child. The parents impose a minute amount of pain on their precious child in order to show their commitment and to help in the process of raising, teaching and perfecting the work of God. Part of the body was left as an unnecessary encumbrance, that in removing, it is as though we are partners with God in creation. Removing the package so to speak.
It also symbolizes the ambiguity of the human body. The organs of reproduction can also be the organs of oppression and need to be ‘tamed.’ First through a symbolic act but then through obedience to the demands of Jewish discipline and Law. The tears of the child are brief. But they remind parents that their task also involves discipline and sometimes making their child cry as well. But that is their sacred tasks. As the Bible says “If you spare the rod (refuse to be strict sometimes) and you spoil the child.”
As for women, their induction comes later with the blood of childbirth. Their commitment to the people is through their bodies ensuring continuity.