Thomas Aquinas, Compendium of Theology

To some extent, Eutyches embraced the error of these heresiarchs. He taught that there was one nature common to both God and man after the Incarnation. However, he did not hold that Christ was lacking in soul or in intellect or in anything pertaining to the integrity of nature.

The erroneousness of this theory is plainly apparent. The divine nature is perfect in itself, and is incapable of change. But a nature that is perfect in itself cannot combine with another nature to form a single nature unless it is changed into that other nature (as food is changed into the eater), or unless the other nature is changed into it (as wood is changed into fire), or unless both natures are transformed into a third nature (as elements are when they combine to form a mixed body). The divine immutability excludes all these alternatives. For neither that which is changed into another thing, nor that into which another thing can be changed, is immutable. Since, therefore, the divine nature is perfect in itself, it can in no way combine with some other nature to form a single nature.

Moreover, as we see if we reflect on the order of things, the addition of a greater perfection causes variation in the species of a nature. Thus a thing that not only exists but lives, for example, a plant, differs in species from a thing that merely exists. And that which exists and lives and feels, for instance, an animal, differs in species from the plant, which merely exists and lives. Likewise a being that exists, lives, feels, and understands, namely, a man, differs in species from the brute animal, which merely exists, lives, and feels. Accordingly, if the single nature which the Eutychean theory ascribes to Christ has the perfection of divinity in addition to all these other perfections, that nature necessarily differs in species from human nature, in the way that human nature differs specifically from the nature of a brute animal. On this supposition, consequently, Christ would not be a man of the same species as other men, a conclusion shown to be false by Christ's descent from men according to the flesh. This is brought out by Matthew in his Gospel, which begins with the words: "The book of the generation of Jesus Christ, the son of David, the son of Abraham," and so on.