Mirroring what tasogare said: There are a lot of research professors who will not give you the flexibility of finding the question. They often are paying you to be an RA, and will want you to work on their topics, not yours.

This may vary per discipline. In the circles I was in, this was the norm, though. Some professors were open to you choosing your own topic, but the "contract" was similar: If they are funding your research, then you should work on your own topic "on your own time".