The girlfriend thing is an excuse and probably not even true, but that doesn't mean his reasons were sinister. Just naive, insensitive and... primitive, I guess? He was clearly going for "controversial humour" like, say, Frankie Boyle, with the problem being that it wasn't a very
clever attempt at controversial humour. I'm a fan of controversial humour and this video just wasn't funny... not because it was offensive to me or upset me in any way... just because it straight up WASN'T funny. It was basic, longwinded and boring. I guess that's where the problem lies? When you use something controversial in an attempt at dark humour, and it isn't actually FUNNY at all, then all you're left with is the words themselves and their very real associations.
So yeah, he just wanted to post something controversial in an attempt at being funny and gaining some "internet fame", and being clearly unimaginative, he thought "Hmmm what's controversial? Nazis. I'll say something about Nazis and Jews derp lolol". It's just the first thing he thought of. On another day he might have thought of a different "generic controversial topic" and had the dog respond to that. I don't think he really gave that part much thought at all.
Ironically, it wouldn't have gained anything like the traction or notoriety that it did if it had just been left alone as another crappy YouTube video. The police and press attention has resulted in the original youtube video getting nearly 2 million jews