As many a 12-year-old boy has observed, the German shepherd is a badass dog. That's kind of their whole point. But a counterintuitive fact about the world is that, taken as a whole, cats are actually way more badass than dogs. Compare lions, panthers, and tigers to coyotes, wolves, and the large dog whose bellies you've amiably patted. There's no contest.
For an illustration of this concept, look no further than the video above. In it, a German shepherd at the zoo gets a little fresh with a cougar behind a glass partition. The cougar then takes action, and the interaction is far more satisfying than noted movie-that-came-out-in-2001 Cats & Dogs.
At about five seconds in, the dog seems to like his chances against the monstrous cat, but soon faces facts and spends the next minute and 55 seconds cowering as the cougar flexes on him. Thankfully, there's a pane of glass there -- but what a terrible zoo that would be if there weren't.
Anyway, go hug your dog.