Sometimes people use "respect" to mean "treating someone like a person," and sometimes they use "respect" to mean "treating someone like an authority."
And sometimes people who are used to being treated like an authority say, "if you won't respect me, I won't respect you," and they mean "if you won't treat me like an authority, I won't treat you like a person."
And they think they're being fair but they aren't, and it's not okay.