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.
I most often use Respect in the sense of Legitimate other, but I acknowledge I don’t always take it as far as feeling the connection to the other person.
In my professional occupation, Respect is frequently applied to a person’s capabilities, skills and approach.
When paired with “but”, the word Respect can be damning.