For those who do it and say it is Islam it is their Islam.
However there are only a few allegedly weak hadiths prescribing the practice.
Al-Azhar University has though made several fatwas on it through times either declaring it fard or sunnah. And that is to my knowledge also the orthodox stance in the four Sunni madhabs, Despite that very large populations of Muslims have never practiced FGM especially in Pakistan and India where I only know of reports from the small Bohra minority where activists try to stop the practice.
These days Al-Azhar condemns it but when the Muslim Brotherhood was in power in Egypt Morsi reportedly wanted Al-Azhar to change its position again.
It is also practiced by Christians and animists in large numbers in Africa. And the worst kind is named "Pharaonic" (mostly used in Egypt, Sudan and Somalia to my knowledge) where everything are cut out and the girl is sewn together again. I doubt it would be called "Pharaonic" if it was tied 1:1 to Islam.
Kurds are also known to do it so it is not tied solely to the upper half of Africa and happens on the Arab peninsula too.
In Indonesia a "light" form of FGM is widely practiced among the Muslim population. I think I read somewhere that it was unheard of there until Islam came. So they probably adopted it from the cool Arab kids they traded with.
Here is a short documentary about FGM in Iraqi Kurdistan worth watching.
https://www.youtube.com/watch?v=DHLf0bOJwZMRegarding your teacher I would look at the non-Muslim practices of FGM prevalent in Africa.
And the Kabaa has non-Islamic origins. Except if you buy that Abraham placed it there and Abraham was Muslim, of course.