[This post assumed what I still take to be the common or usual notion of “authority” as something that is supposed to be unconditionally binding under some circumstances. It does not apply to a notion of authority that would be always symmetrically balanced by reciprocal responsibility, and therefore always defeasible.]
Authority is a poor substitute for reason. It gives us ready-made conclusions that may be true, but are without justification. When we have reason and reasons, we have no need to be guided by authority.
Respectable authors have nonetheless talked about rational authority. The idea is that reasons should have something like a sort of authority over us. That is fine, as long as we recognize it as a metaphor or simile rather than a literal truth.
The difference is, precisely, that authority operates fundamentally in registers of will, compulsion, and obedience. Authority at its core does not answer to reasons. “Do it because I said so!” or just “Obey!” is its first and last move. Obedience to authority is characterized by heteronomy rather than autonomy, in Kant’s sense of those terms.
We may be freely “compelled” only by reasons, when we genuinely find them to be genuinely convincing. That is very different from someone compelling us, or from our having internalized an external compulsion. (See also Euthyphro; Necessity in Normativity; Binding; Deontic; Enlightenment.)