Why does all my body fat go on my stomach?

That's the location where the stored calories could be most easily carried.

Humans who carried their adipose tissue at their extremities would have to spend a lot more calories to move them around, since the angular momentum would be significantly more. Imaging holding a sledge hammer by the end of the handle. Rotating it through a quarter circle back and forth is hard. If you hold it from the sledge end and rotate the handle it's a lot easier to do that.

Your legs/arms are the same way, which is why your body is shaped with minimal heavy bits at the ends with more and more of the heavy bits concentrated near your center.

In the body, you've got your essential fat, which is mostly in your internal organs, and then scattered around the rest of the body pretty evenly, then your adipose tissues, which are pretty much just stored calories and are concentrated on the torso until you get into cases of extreme obesity.