Question

why are equal amounts of a weak acid and its conjugate base a good buffer?

Answer 1

It's not equality that is important, but LARGE amounts of both. That way, when some extra acid is added, there is lots of conjugate base to react with it and absorb it, and when some extra base is added, there is lots of the weak acid to reach with it and absorb it. So either way, extra acid or base gets absorbed.

It just so happens if you have large amounts of both, then you pretty much have fairly equal amounts of both, too. I mean, 1 M acid and 0.1 M conjugate base is a perfectly reasonable buffer, although 1 M acid and 1 M base would be better, because you have more base to suck up any added acid. But the important point is that it's not 1 M acid and 0.0000001 M conjugate base. That would be a useless buffer.