Sometimes the person doing the muting is being childish, sometimes the person being muted is being childish, and sometimes both are. But it's all subjective.

What should be done if half the people think that the person doing the muting is obviously wrong and should apologize, and half the people think that the person being muted is obviously wrong and should apologize?

There is no good answer to that, under the current mute system.

Splitting the discussion in half doesn't scale, among worse problems. Not commenting... Well, that basically ends up with "the poweruser is king" (as they tend to be the people posting) - and if you need evidence that that has problems, look at StackOverflow.

Effectively, mute ends up making the site turn into a bunch of echo chambers that don't ever communicate with each other.

And as such, I do not believe that the censorship portion of muting should exist.

Mute should be the comment equivalent of ignore, and no more. You don't see the comments of a user you ignore, but other people do.