John of Damascus explains in book 3 their problem, and the solution.
OOs believe in a dialectic in the definition of nature.
It either means a compendium, or a subsistence.
Now Christ can’t assume a compendium, since that would draw many hypostases into a union, and also not subsistence, because the human nature is not independent of the Word prior to the union: it gets existence through the union itself.
So John says the nature assumed is neither the abstraction, compendium, or subsistence, but nature as viewed in the subsistence, which is a category OOs lack.
“Nature is regarded either abstractly as a matter of pure thought (for it has no independent existence): or commonly in all subsistences of the same species as their bond of union, and is then spoken of as nature viewed in species: or universally as the same, but with the addition of accidents, in one subsistence, and is spoken of as nature viewed in the individual, this being identical with nature viewed in species. God the Word Incarnate, therefore, did not assume the nature that is regarded as an abstraction in pure thought (for this is not incarnation, but only an imposture and a figment of incarnation), nor the nature viewed in species (for He did not assume all the subsistences): but the nature viewed in the individual, which is identical with that viewed in species. For He took on Himself the elements of our compound nature, and these not as having an independent existence or as being originally an individual, and in this way assumed by Him, but as existing in His own subsistence. For the subsistence of God the Word in itself became the subsistence of the flesh, and accordingly “the Word became flesh John 1:14 ” clearly without any change, and likewise the flesh became Word without alteration, and God became man. For the Word is God, and man is God, through having one and the same subsistence. And so it is possible to speak of the same thing as being the nature of the Word and the nature in the individual. For it signifies strictly and exclusively neither the individual, that is, the subsistence, nor the common nature of the subsistences, but the common nature as viewed and presented in one of the subsistences.”