Does my teacher have any right to do this?

Yes, it’s normal and fair. Not every professor will do it, but many do. Some professors don’t even talk about some of the material on the test. It’s in the reading or on assignments, and you’re expected to learn it on your own and ask questions if you need help. I knew a professor once that wanted to teach a section of the material during the first half of the final exam time and then include that material on the exam that students would take during the second half of the final exam time. We (the TAs) talked her out of it because we all thought that was a little ridiculous, but professors can structure their class however they want.

Also, in classes where we’ve had reviews before exams, they were typically held outside of class time because there just wasn’t enough time to cover all the material and hold a review. But I also went to a school on the quarter system where there was a little more time pressure.