"What right has one person to teach another" - it's not a question of one person having a right to teach other people. There's a duty to pass on the knowledge and skills to the people who want them and need them. And we all have a duty to seek out the knowledge and skills we need.

"I have a right to teach you to play the guitar" - it wouldn't seem to make much sense to say something like that. "If you want to play the guitar, I can teach you" would make sense. It might even make sense to say "It is my job to try to teach you to play the guitar and that is what I am going to do."

I think it often makes things much clearer to leave aside talk about rights, and talk about reciprocal duties. (So in Civil Right terms it wouldn't have been "I have a right to be served at this lunch counter" but rather "You have a duty to serve me - and I have a duty to insist that you serve me.")