First of all, you don't know "why" a term like "Theotokos" does not appear in the NT, any more than you know "why" a term like "Sola Scriptura" or "Sola Fide" does not appear.
"Other children of Mary" and "sons of Mary" --- these terms are absent as well.
Bottom line, nothing can be dispositively proven, one way or the other, merely by the lack of a later term in an earlier text.
"Mother of God" means nothing more than "Mother of Jesus who is God." It has no demigoddess implications whatsoever
Any reasonable person would know this, and wouldn't have to have it explained to them over and over again, if they would be so good as to look up the actual historic context --- the Council of Ephesus.
Ephesus' definition of "Mother of God" ("Theotokos") was essentially Christological: it clarified and confirmed that Jesus Christ is One Divine Person, not two. And it was accepted with gratitude by the entire Christian Church: the churches now known as Catholic, Eastern Orthodox, Coptic, Ethiopian, Armenian, Syriac, Eritrean, etc.
It was only considered controversial by the Nestorians, because they taught, erroneously, that Jesus is two separate Persons, one Divine and one Human.
That's why the Nestorians, alone, could not agree that Mary is the Mother of God. They did not believe that Jesus, all through His existence, and even in his mother's womb, was God.
You could look it up. That's not too much to ask.
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