Sportsmanship is also listed as a moderation badge in the list of badges, perhaps because voting up is considered 'moderation' on Stack Exchange, and an important one (it's even mentioned in the tour). I guess it's equally valid to regard it as an answer badge.
Why was it chosen? It turns out that it was the initiative of a community (Mathematics Stack Exchange) which was then adopted by the company:
The purpose of counting these badges is to approximately quantify the contributions that do not result in reputation (edits, votes, meta posts, tagging, reviewing) as well as the level of experience with the site.
Upvoting competing answers doesn't give reputation (it can even hinder gaining reputation, because you're giving your own answer less visibility).
100 answers alone is not a small feat.
True, but you don't need to have posted 100 positively-scoring answers; if (on a question where you have a positively-scoring answer) you upvote n other answers, this will count n times towards the badge. (I think this is unfortunate, but as explained in the comments here that it won't be changed.)
Personally, I don't care if a moderator has 10 answers or 10000 answers. A moderator's role is to moderate not answer questions.
That's certainly true (proof), but past elections across the network have shown reputation (and candidate score) have a large effect on whether a candidate is elected or not. On Stack Overflow, you have almost no chance to win unless your score is 40/40.