Wouldn't it then follow that all students of the same teachers end up with the same skill level in math? Not sure that's the case.
You’re making an argument somewhat along those lines, but given that I didn’t stipulate a convergence condition your conclusions can be dismissed by me.
If it were a valid argument then we’d need Gödel.
In other words: Some students flourish despite their teachers, some flourish because of them.
A bad teacher instead gives you a bimodal distribution and just doesn't bother teaching those students.