Objection 1. It seems that circumcision was instituted in an unfitting manner. For as stated above (Article 1) a profession of faith was made in circumcision. But none could ever be delivered from the first man's sin, except by faith in Christ's Passion, according to Romans 3:25: "Whom God hath proposed to be a propitiation, through faith in His blood." Therefore circumcision should have been instituted forthwith after the first man's sin, and not at the time of Abraham.
Objection 2. Further, in circumcision man made profession of keeping the Old Law, just as in Baptism he makes profession of keeping the New Law; wherefore the Apostle says (Galatians 5:3): "I testify... to every man circumcising himself, that he is a debtor to do the whole Law." But the observance of the Law was not promulgated at the time of Abraham, but rather at the time of Moses. Therefore it was unfitting for circumcision to be instituted at the time of Abraham
Objection 3. Further, circumcision was a figure of, and a preparation for, Baptism. But Baptism is offered to all nations, according to Matthew 28:19: "Going... teach ye all nations, baptizing them." Therefore circumcision should have been instituted as binding, not the Jews only, but also all nations.
Objection 4. Further, carnal circumcision should correspond to spiritual circumcision, as the shadow to the reality. But spiritual circumcision which is of Christ, regards indifferently both sexes, since "in Christ Jesus there is neither male nor female," as is written in Colossians 3 [Galatians 3:28]. Therefore the institution of circumcision which concerns only males, was unfitting.
On the contrary, We read (Genesis 17) that circumcision was instituted by God, Whose "works are perfect" (Deuteronomy 32:4).
I answer that, As stated above (Article 1) circumcision was a preparation for Baptism, inasmuch as it was a profession of faith in Christ, which we also profess in Baptism. Now among the Fathers of old, Abraham was the first to receive the promise of the future birth of Christ, when it was said to him: "In thy seed shall all the nations of the earth be blessed" (Genesis 22:18). Moreover, he was the first to cut himself off from the society of unbelievers, in accordance with the commandment of the Lord, Who said to him (Genesis 13:1): "Go forth out of thy country and from thy kindred." Therefore circumcision was fittingly instituted in the person of Abraham.
Reply to Objection 1. Immediately after the sin of our first parent, on account of the knowledge possessed by Adam, who was fully instructed about Divine things, both faith and natural reason flourished in man to such an extent, that there was no need for any signs of faith and salvation to be prescribed to him, but each one was wont to make protestation of his faith, by outward signs of his profession, according as he thought best. But about the time of Abraham faith was on the wane, many being given over to idolatry. Moreover, by the growth of carnal concupiscence natural reason was clouded even in regard to sins against nature. And therefore it was fitting that then, and not before, circumcision should be instituted, as a profession of faith and a remedy against carnal concupiscence.
Reply to Objection 2. The observance of the Law was not to be promulgated until the people were already gathered together: because the law is ordained to the public good, as we have stated in I-II, 90, 2. Now it behooved the body of the faithful to be gathered together by a sensible sign, which is necessary in order that men be united together in any religion, as Augustine says (Contra Faust. xix). Consequently, it was necessary for circumcision to be instituted before the giving of the Law. Those Fathers, however, who lived before the Law, taught their families concerning Divine things by way of paternal admonition. Hence the Lord said of Abraham (Genesis 18:19): "I know that he will command his children, and his household after him to keep the way of the Lord."
Reply to Objection 3. Baptism contains in itself the perfection of salvation, to which God calls all men, according to 1 Timothy 2:4: "Who will have all men to be saved." Wherefore Baptism is offered to all nations. On the other hand circumcision did not contain the perfection of salvation, but signified it as to be achieved by Christ, Who was to be born of the Jewish nation. For this reason circumcision was given to that nation alone.
Reply to Objection 4. The institution of circumcision is as a sign of Abraham's faith, who believed that himself would be the father of Christ Who was promised to him: and for this reason it was suitable that it should be for males only. Again, original sin, against which circumcision was specially ordained, is contracted from the father, not from the mother, as was stated in I-II, 81, 5. But Baptism contains the power of Christ, Who is the universal cause of salvation for all, and is "The Remission of all sins" (Post-Communion, Tuesday in Whitweek).
Source: Summa Theologica (New Advent)