Here's an analogy: take a point on the sphere and consider the set of points on the sphere that are distance d from that point. The size of that set increases as d goes from 0 to 1/4 * circumference, then decreases as d goes to 1/2 * circumference, and you end up with just the antipodal point.
There's probably some general argument that you'll always see this with any sufficiently nice compact metric space.
There's probably some general argument that you'll always see this with any sufficiently nice compact metric space.