Thomas Aquinas

“ As Christ voluntarily took upon Himself our death, which is the effect of sin, whereas He had no sin Himself, in order to deliver us from death, and to make us to die spiritually unto sin, so also He took upon Himself circumcision, which was a remedy against original sin, whereas He contracted no original sin, in order to deliver us from the yoke of the Law, and to accomplish a spiritual circumcision in us---in order, that is to say, that, by taking upon Himself the shadow, He might accomplish the reality.
Art. 2 - Whether His name was suitably given to Christ? ”

“ But a victim should not be offered up for a victim. Therefore it was not fitting that another victim should be offered up for Christ.
Objection 4: Further, among the legal victims the principal was the lamb, which was a "continual sacrifice" [Vulg.: 'holocaust'] , as is stated Num. 28:6: for which reason Christ is also called "the Lamb---Behold the Lamb of God" (Jn. 1: 29) . It was therefore more fitting that a lamb should be offered for Christ than "a pair of turtle doves or two young pigeons." ”

“ Moses seems to have chosen his words in order to exclude uncleanness from the Mother of God, who was with child "without receiving seed." It is therefore clear that she was not bound to fulfil that precept, but fulfilled the observance of purification of her own accord, as stated above.
Reply to Objection 3: The sacraments of the Law did not cleanse from the uncleanness of sin which is accomplished by grace, but they foreshadowed this purification: for they cleansed by a kind of carnal purification, from the uncleanness of a certain irregularity, as stated in the [4194] FS, Q [102] , A [5] ”

“ Further, "every action of Christ is a lesson to us" [*Innoc. III, Serm. xxii de Temp.] ; wherefore it is written (Jn. 3:15) : "I have given you an example, that as I have done to you, so you do also." ”

“ The law ofLev. 12:6, 8 "commanded those who could, to offer, for a son or a daughter, a lamb and also a turtle dove or a pigeon: but those who were unable to offer a lamb were commanded to offer two turtle doves or two young pigeons" [*Bede, Hom. xv in Purif.] . "And so the Lord, who, 'being rich, became poor for our [Vulg.: 'your'] sakes, that through His poverty we [you] might be rich," as is written 2 Cor. 8:9, "wished the poor man's victim to be offered for Him" just as in His birth He was "wrapped in swaddling clothes and laid in a manger" [*Bede on Lk. 1] . ”