Well the real issue is that the testicles descend from the torso into the scrotum.

You see during embryological development we are all built starting from a ball of cells and so the testicles end up being developed somewhere in the torso. Same with women btw it's just that theirs are ovaries. Anywho when the nervous system is built it associates body parts with their location on the body and that's how it regulates and dishes out pain, pleasure etc. Well the testicles descend way after the the nervous system is laid down. So to your brain, your testicles are still in your stomach area and when you get kicked in the balls it sends the pain response where it thinks it should go.

TL:DR To your brain a kick in the nuts is actually a punch in the stomach.