"He is my professor."
Translation:Він мій викладач.
Not sure what you mean. You suggesting Мій уикладач? That would't work. The B-У interchange within a word happens when B is followed by a consonant. (вночі - уночі, вниз-униз..)
I wanted to note that we use the word вчитель in school and the word викладач for any teacher in uni. Викладач does not mean someone who gained a title of professor. It would be професор.
I believe it hasn't been explained anywhere