The Bible teaches that there is a total and permanent distinction between the Creator
and the creation. God is transcendent and not dependent on the creation, but made it
out of nothing. On the other hand, having been created, the matter of the
world (including humans like Jesus Christ) really has a real independent existence
and is not mere illusion.
So even in the person of Jesus Christ,
these two natures: the divine and human, coexisted "without conversion, composition
or confusion", as the Westminster Confession of Faith puts it. This compact statement rejects several plausible but
ultimately untenable alternatives:
a) conversion: Some early sects taught that Christ had a single nature that changed before and after the Incarnation; Christ was divine, then was born as a purely human being; then was transformed back into a divine being after the Resurrection. This teaching fails to account for Jesus' statements about his relationship with the Father before the world existed.
b) composition: The two natures were "blended" in some way to form one person. This violates the basic doctrine that Creator and creature must be kept distinct, to avoid the error of pantheism.
c) confusion: The two natures were not really distinct, but oscillated or interacted in some mysterious way. This view leaves the doctrine of the two natures in an unstable or dynamic state.
In the course of church history, after a series of ecumenical councils the church settled the issue by reiterating what most Christians had always held, namely that there are two distinct natures [hypostases] in Christ; both are real and one does not dominate the other. See the 3D Overview for more details on this historical development.