The Fathers surely knew what they were saying! Let’s look at the Council of Chalcedon in AD 451 which formulated the Chalcedonian Creed, from where we get the hypostatic union that you’re talking about. I may have skipped over some repetitive parts:
Following, then, the holy Fathers, we all unanimously teach that our Lord Jesus Christ is to us One and the same Son, the Self-same Perfect in Godhead, the Self-same Perfect in Manhood…
The Fathers have taught that Christ is a
single Being. There are not two Christs, and the single Christ is exactly the same in being man and God at once. That’s a summary of the hypostatic union.
the Self-same of a rational soul and body; co-essential with the Father according to the Godhead, the Self-same co-essential with us according to the Manhood; like us in all things, sin apart…
Christ has both a rational soul and body, just like we do. He is of the same essence as the Father, being God (see
Council of Nicaea), and he is the same as us in all things (cf. Hebrews 4:5) save for the fact that He never did sin.
before the ages begotten of the Father as to the Godhead, but in the last days, the Self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the Manhood…
He is eternally begotten of God the Father, being God the Son, but eventually undertook a human nature for the sake of our salvation, being born of Mary. The next quotes are probably the most important parts, what the Fathers are trying to tell us overall.
acknowledged in Two Natures unconfusedly, unchangeably, indivisibly, inseparably…
These two natures are not “mixed up” and they remain distinct. One does not take over the other in any way. They are not some combination thereof (e.g., Apollinarianism, Monophysitism/Eutychianism, Monothelitism, Miaphysitism).
the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved…
Both natures are distinct. We can tell that Christ is both human and divine, we don’t need to say that there is some “new nature” as some of the heresies I’ve listed above do.
and (both) concurring into One Person and One Hypostasis; not as though He were parted or divided into Two Persons, but [the] One… Jesus Christ…
The Lord Christ is one, singular. His two natures, divine and human, do not make Him a new Being. To say otherwise would be Nestorianism.