The "right answer" consisting of a valid proof is very different from the "right answer" to a numerical computation. The thinking and communication process is surely more relevant to the former than the latter. And if anything, as you say, the former is what math is really about.
When it comes to mathematics, the exact form of the outcome isn't very important. Maybe it's a valid proof in one case, maybe it's a specific number in another case.
It's the degree of rigor that's important. Rigor is what separates mathematics from other fields of study.
Thinking and reasoning about abstract concepts aren't without value, of course. But if this is done without an extreme degree of rigor, it probably should not be considered to be mathematics.
A: Because they can't tell their coffee cup and donut apart.
When it comes to mathematics, the exact form of the outcome is extremely important. Proofs that are aesthetically pleasing are better than proofs that are not. Proofs that glean insight are better than proofs that do not. In fact, most people don't care about whether a theorem is true unless the proof provides sufficient insights.