It may sound odd (or even blasphemous) to say that Jesus Christ is not a human person, but this is precisely true. The problem is that this is a very metaphysically precise statement and most people have not been introduced to the relevant philosophical distinctions required to make proper sense of it. Here I will try to explain these in as simple manner as I can. The biggest hurdle is usually to understand that:
Persons are not natures – persons HAVE natures.
If it is said that, “Jack is a human” we can see that somehow “Jack” and “human” are distinct. If Jack and human were identical, then “Jack is a human” would mean “Jack is a Jack” or “Human is a human” which would be circular and pointless things to say. However, we understand that “Jack is a human” means something: that “Jack has a human nature” or more precisely, “Jack, a person, has a human nature.” Understood this way we can see more clearly that to be a person and to have a nature are not equivalent.
An easy way to think of this is that “person” refers to WHO something is and “nature” refers to WHAT something is.
The next thing we need to grasp is that to be a person is not necessarily to be a human being (i.e., a person with a human nature). A person is just a rational being (one having intellect and will). But things other than humans are rational beings. Angels are persons and so is God. So two persons may have different natures (they can both be persons but be different things).
This is where Christian doctrine gets complicated.
The doctrine of the Trinity says that with God there are THREE PERSONS (three “WHOS”: Father, Son, Holy Spirit) – in ONE NATURE (one “WHAT”: divinity). So here we have three distinct persons (who are not each other!) sharing a single nature. That is why Christianity is monotheistic: we believe in only one God even though three separate persons are that God.
The doctrine of the Incarnation says that with Jesus Christ there is ONE PERSON (one “WHO”: the Son) in TWO NATURES (two “WHATS”: divinity and humanity). So here we have only one person who has two natures.
Now, because Jesus Christ is God, his personhood is united forever to his divine nature and that did not change at the Incarnation (because God cannot change). Instead of changing “into” a human, Jesus assumed an additional human nature (intellect, will, and body) but Jesus did NOT assume an additional human person. Jesus Christ did not become two people – he remained one person (a divine person). Although human natures and human persons typically go together one-to-one (i.e., every human person has a human nature and vice versa), it is not metaphysically necessary that they do so. In the case of the Incarnation a “personless” human nature was added to the divine person of Jesus Christ such that he now has a human nature as well.
Thus, it is true to say that Jesus Christ is a human being (because he is a person with a human nature), but it is false to say he is a human person (because his human nature did not generate a new person).