Objection 1. It would seem that the Son of God ought to have assumed human nature abstracted from all individuals. For the assumption of human nature took place for the common salvation of all men; hence it is said of Christ (1 Timothy 4:10) that He is "the Saviour of all men, especially of the faithful." But nature as it is in individuals withdraws from its universality. Therefore the Son of God ought to have assumed human nature as it is abstracted from all individuals.
Objection 2. Further, what is noblest in all things ought to be attributed to God. But in every genus what is of itself is best. Therefore the Son of God ought to have assumed self-existing [per se] man, which, according to Platonists, is human nature abstracted from its individuals. Therefore the Son of God ought to have assumed this.
Objection 3. Further, human nature was not assumed by the Son of God in the concrete as is signified by the word "man," as was said above (Article 3). Now in this way it signifies human nature as it is in individuals, as is plain from what has been said (3). Therefore the Son of God assumed human nature as it is separated from individuals.
On the contrary, Damascene says (De Fide Orth. iii, 11): "God the Word Incarnate did not assume a nature which exists in pure thought; for this would have been no Incarnation, but a false and fictitious Incarnation." But human nature as it is separated or abstracted from individuals is "taken to be a pure conception, since it does not exist in itself," as Damascene says (De Fide Orth. iii, 11). Therefore the Son of God did not assume human nature, as it is separated from individuals.
I answer that, The nature of man or of any other sensible thing, beyond the being which it has in individuals, may be taken in two ways: first, as if it had being of itself, away from matter, as the Platonists held; secondly, as existing in an intellect either human or Divine. Now it cannot subsist of itself, as the Philosopher proves (Metaph. vii, 26,27,29,51), because sensible matter belongs to the specific nature of sensible things, and is placed in its definition, as flesh and bones in the definition of man. Hence human nature cannot be without sensible matter. Nevertheless, if human nature were subsistent in this way, it would not be fitting that it should be assumed by the Word of God. First, because this assumption is terminated in a Person, and it is contrary to the nature of a common form to be thus individualized in a person. Secondly, because to a common nature can only be attributed common and universal operations, according to which man neither merits nor demerits, whereas, on the contrary, the assumption took place in order that the Son of God, having assumed our nature, might merit for us. Thirdly, because a nature so existing would not be sensible, but intelligible. But the Son of God assumed human nature in order to show Himself in men's sight, according to Baruch 3:38: "Afterwards He was seen upon earth, and conversed with men."
Likewise, neither could human nature have been assumed by the Son of God, as it is in the Divine intellect, since it would be none other than the Divine Nature; and, according to this, human nature would be in the Son of God from eternity. Neither can we say that the Son of God assumed human nature as it is in a human intellect, for this would mean nothing else but that He is understood to assume a human nature; and thus if He did not assume it in reality, this would be a false understanding; nor would this assumption of the human nature be anything but a fictitious Incarnation, as Damascene says (De Fide Orth. iii, 11).
Reply to Objection 1. The incarnate Son of God is the common Saviour of all, not by a generic or specific community, such as is attributed to the nature separated from the individuals, but by a community of cause, whereby the incarnate Son of God is the universal cause of human salvation.
Reply to Objection 2. Self-existing [per se] man is not to be found in nature in such a way as to be outside the singular, as the Platonists held, although some say Plato believed that the separate man was only in the Divine intellect. And hence it was not necessary for it to be assumed by the Word, since it had been with Him from eternity.
Reply to Objection 3. Although human nature was not assumed in the concrete, as if the suppositum were presupposed to the assumption, nevertheless it is assumed in an individual, since it is assumed so as to be in an individual.
Source: Summa Theologica (New Advent)