I think it involves an error with regards to the union of Christ’s human and divine natures. I’m not really sure of the details, but I believe it either denies or at least considerably mischaracterizes the hypostatic union.
At the time (early 5th century) a lot of the Church’s Christology was being hammered out. There was a lot of debate about how many natures Christ had and how those natures interacted.
For Nestorius, the union between Jesus’ divine and human natures was merely a moral union (rather than the true, hypostatic union), which is what led him to assert things (like (name removed by moderator) points out above) that Christ is the son of God by adoption rather than by nature.
It’s also what led him to deny the title of “Theotokos” (i.e. Mother of God or “Godbearer”) for Mary. For Nestorius, Mary was the Mother of Jesus and his human nature. But without believing those natures to be intimately united in the hypostatic union, he didn’t think it proper to refer to her as the Mother of God.
In a sense, a lot of present day Protestant objections to this title of Mary are a bit Nestorian. If Jesus is God and Mary is the mother of Jesus, then Mary is the Mother of God. The only way to deny that is to introduce separation between the divine and human natures of Jesus.
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