Pope Leo’s Letter 28 was a watershed moment in orthodox Christology, but there is a long history of teaching his conclusion while leaving off his reason. The conclusion is the dual human and divine natures of Christ, united without confusion (that is, they aren’t united in such a way as to form a third nature other than the two) and distinct without division (that is, they’re separate without belonging to what would be later called different persons).
But to simply assert different natures in Christ is ad hoc and unpersuasive. “Nature” has always had a whole spool of meanings, many which have fuzzy edges, and the use of the term can start to feel suspiciously like trying to cram revealed mysteries into philosophical preconceptions. Leo’s case is better than this. He starts with the fact that when one thing is born of another, they’re in one sense the same thing (call it the A sense of “thing”) and in another sense different things (call it B). The “A” sense gives us the cluster of descriptions species, essence, sort of thing, family (in both its social and classificatory sense) and the first meaning of nature. The B sense gives us the cluster of descriptions individual, particular, or (in the case of things with minds) person or self. There is also another class of words that are more general than the A and B sense, but which in any particular usage might mean only the A or B sense. “Thing” is obviously one of them, but so are substance, entity, being, something etc. Call this sense C of ‘thing”.
But – and here’s the crucial axiom – the heart of creedal Christology is that Jesus has two births. The first thing we affirm about him is that he is Son of the Father / born of the Father before all ages, etc. and that he is born of the Virgin. What this means is that Christ is one thing (B) born of two different things (C) who are also different things (A); or (to change up the terms a bit) Christ is a single entity (B) who is the same thing (A) as two different beings (A).
At some point it helps to standardize the terms and avoid the ambiguity of C-class terms, and so we get the familiar formula that Christ is one person in two natures, united without confusion and distinct without separation. This is not so much a theoretical development as simply a clarification of what it would mean to have two births. Asserting that the natures were “confused” (mixed together to form a tertium quid) would mean that he wasn’t the same thing (A) as his father or mother, and therefore that he was not born of either of them. We likewise insert the “distiction” clause to clarify that it is the same being (B) that is born of the father and of Mary, since without this it make no sense at all to talk about him having two births. The “One person two natures” formula simply follows a priori from one being having two births.
It’s just this birth language that tends to get left off of most discussion of what Christ is. This occludes not only the reason why we speak of two natures in one person, but also the way in which we are called to be like Christ. Note that Christ is the paradigm case of being “born again” – it is precisely because Jesus, eternally born of the Father, was born again of Mary by the Holy Spirit that we might be also born again by the Spirit into union with the Father. The Incarnation is not some divine trick done once but a paradigm of how all creation will be born again to the Father in Christ by the Holy Spirit. In insisting that Christ is one person in two natures we are not merely doing tiresome apologetics, or working in the advance of some supposed Nicene “Hellenism” – we’re proclaiming the one chance creation has to find its way back to the Father.