Because they (the ATF) said so.
It goes back to 1934. The National Firearms Act was passed to make the illegal behaviors of bank robing gangs more illegal by outlawing their guns of choice. Short rifles and shotguns being among those.
In the end it isn't going to make sense. That is the best way I can explain it.
Stopping power: The power some guns have to make you stop what you are doing and get your wallet out.