As rough-going as Christology can be, the hardest element of it is explaining how Christ can have a complete, individual human nature and yet not be a human person. The logical responses are relatively easy to come by, here I’ll give two reasons for wanting it to be the case, and one response to a common objection.
1.) The lex orandi. To make Christ two persons will change how we pray to him, and what we would expect to find of him in the Scriptures, which would perhaps work their way up to Christ referring to himself as “we” and the disciples falling down before him as y’all. Prayers to Christ would be addressed both to a saint (pray for us) and to a divinity (have mercy on us).
2.) The eschatological. Christ, being “born of the Father before all ages”, was the first to be “born again” into temporal and corruptible life. This allows our own corruptibility to be the mirror image of his own, so that we might be born again so to “become participants in the divine nature, having escaped the corruption of the world”. Just as we will not be a different person who puts on the divine nature, so too Christ cannot be a different person for putting on human nature.
3.) The “like us in all ways”. To say that Christ is “like us in all ways” could never have meant that he is the same person as us. Neither can we speak about “having” a human person, since a person is only something someone can be.