Let's break it down.
What is fighting, essentially? Human/Humanoid creatures that have been trained in martial arts to identify and attack weak points in the human anatomy, such as the head, liver, groin, neck etc.
Insects (or just bugs in this case) have far different physiological traits and therefor weaknesses than humans. This would make someone (or something) that has been trained in martial arts have a really hard time bringing down an opponent that has an anatomy which it wasn't trained for.
Furthermore, most bugs have something called an exoskeleton, which is a layer of a hard substance that covers their entire bodies (and vital organs) from trauma such as a punch or a kick etc.
Now that might make you think "why is Bug weak to Rock?" and I guess the answer for that would be because of the idea that when someone sees a cockroach (example,this applies to any creepy-crawly) most people's immediate reaction would be to pick something hard like a shoe or a rock and smash it, rather than hitting it with a karate chop or a body slam.
You made a point that hitting a bug with your hand or foot would kill it, and you are correct. However this is the Pokemon world we're talking about here, where most bugs are about the size of a small car or a person. Good luck smashing something like that with the palm of your hand...
In the end, only Game Freak can tell you why they decided to make Bug resist Fighting, anything else is speculation. Including this answer. I hope I helped!