a. A person is a (primary) substance of a rational nature. (Boethian definition)
b. There is only one person in Christ, the Word, the Second Person of the Trinity. (Rejection of the heresy of Nestorius, according to which in Christ there are two persons in two natures rather than one person in two natures, as orthodoxy maintains.)
c. The individual(ized) human nature of Christ is a primary substance of a rational nature.
d. Every (primary) substance is its own supposit, which implies that every substance of a rational nature has its own personhood.
I think (c), in particular, requires more work. I am a primary substance of a rational nature, namely, human; but we would not say that my human nature (considered as individualized or not) is a primary substance of rational nature, since it is just what I share with other human beings precisely as human. My human nature is by definition not a primary substance; we aren't talking about primary substances when talking about natures in this way.
If, on the other hand, we take it as a roundabout way of saying 'I am a primary substance of rational nature', and thus take the phrase to mean something like 'the individual of human nature is a primary substance of a rational nature', this becomes true but problematic for treating the tetrad as a inconsistent. Statement (c) is then equivalent to "Christ is a primary substance of human nature, which is a rational nature"; this creates no obvious inconsistency, since we already know from (b) that Christ is a primary substance of rational nature, and combined with the others it merely implies that there is one supposit of Christ, who is the Word and has human nature. (It's not essential here to say anything about supposits; for the purpose in this post, in which it plays no role, we can just treat 'supposit' as a synonym for 'subject', which, despite some differences, is the closest ordinary English word.)
The reason why one would try to put it in terms of individual(ized) human nature is clear enough: what would make the inconsistency would be to establish that the having of a human nature requires having its own supposit. But it is impossible to establish this from human nature considered on its own, so the idea is to try to get out of human nature as individual(ized). However, human nature even as individual(ized) is no more a primary substance than unindividual(ized) human nature; rather, the individual of human nature, that individual thing which has human nature, is a primary substance. The latter breaks the attempt to get a supposit or person specifically for the human nature of Christ, however.