You claim that. Yet none of the most mentally demanding tasks were done by philosophers. Today philosophy is mostly meaningless intellectual posturing. In the past, it was the act of thinking without applying the scientific method. As Feynman said of Spinoza "meaningless chewing around".

If philosophy (and only philosophy) teaches people how to think, then who taught the first philosopher?

No one claimed only philosophy taught people how to think.

How do you know it doesn't just draw out a capacity to think that you already have, and that you could equally well have drawn out by studying or working at something else?

Maybe you could, but that still doesn't make philosophy useless.