Nestorius, the same bishop of Constantinople who refused to call Mary Mother of God was also teaching that Christ was two persons, a divine person and a human person. He believed that the person and nature were the same thing. Since there were two natures in Christ there must also be two persons.

But, what is a person? Boetius gave the enduring classical definition. "A person is an individual substance in a rational nature" or a person is an entity in an intelligent nature. This definition applies to angels, men and God, although the personalities and the intelligent nature of the Trinity far surpasses our own. A person is that which subsists in the nature and cannot be shared with anyone else. It is that which gives identity to a nature.

How do we know that Christ is One Person in two natures?

Christ one day pointed to his personal identity when he asked, "Who do people say that the Son of Man is?" Than he addressed them saying, "But who do you say that I am?" Simon Peter replied, "You are the Messiah, the Son of the living God." (Mt 16:13-16)

The term "Son of Man" points to Christ's humanity, to his mortal nature. It does not specify Christ as an individual but only he who has a human nature in common with the rest of mankind.
The term "Son of God" likewise points to Christ's divine nature but since God has only One Son, this points to his absolute identity. The Son's specific identity is not shared with the Father and Spirit. It is his identity, personality, the Second Person of the Triune God.

Nestorius also taught that the divine and human nature in Christ were united one within the other. God did not become man, rather God the Son resided in the man Jesus in the same manner that God dwells in the just. Since Christ was two persons whose natures were not substantially united, the actions of the Man Jesus could not be attributed to the Son of God. So his birth, suffering and death were only the birth, suffering the death of the Man. If this is the case, mankind was not redeemed because these would be the actions of a mere man. But as it is

"The Divine and the human nature
are united hypostatically in Christ,
that is,
joined to each other in one Person." 84-85

The two natures came together in a single person, God's Son, without losing their properties. On the divine side the Son has the same nature as the Father, eternal and unchanging. On the human side, the nature admits of human growth and enlightenment.

Here we see the twelve year old Christ disputing with the teachers of the law in the temple and it is written "All who heard him were astounded at his understanding and his answers." (Lk 2:47)

Where did boy Christ gain this wisdom? No doubt, some of it from his studies and Jewish culture, but beyond this "by its union to the divine Wisdom, the person of the Word incarnate, Christ enjoyed in his human knowledge the fullness of understanding of the eternal plan he had come to reveal." (Catechism of the Catholic Church, #474)