The belief that Jesus's human and divine natures were not fully united with each other, which implied that Mary could not be the Mother of God, but rather the Mother of Christ.
Athanasius (another bishop) proved to the Church that Arianism did not teach the correct things based off of Jesus, Scriptures, and Tradition.
"We believe in one Lord, Jesus Christ, The only Son of God, Eternally begotten of the Father. God from God, Light from Light, True God from True God. Begotten not made, one in being with the Father. Through him all things were made." -the Creed
St. Cyril of Alexandria (another bishop) proved that Nestorianism was false based on knowledge about Christ, the Scriptures, and Tradition.
"I believe in Jesus Christ...born of the Virgin Mary" -the Creed
Jesus is the only son of God, as said in the Catechism: "When the promised Messiah-King is called "son of God", it does not necessarily imply that he was more than human, according to the literal meaning of these texts. Those who called Jesus "son of God", as the Messiah of Israel, perhaps meant nothing more than this." (441)