It's a joke related to the US veteran healthcare industry. Claims are often denied for not being "service related" even when it seems like they ought to be qualified.
Well, you can shoot a horse, but the issue is that horses are bigger and hardier than people. You'd do a bit of harm, but not necessarily kill it, and even if you did serious damage, a man with a dying horse is much more dangerous than a horse with a dying man, you know?