Okay, it's time to address the elephant in the room. Ooh, err.
"Fasz" on its own is a succinct, cunt-level offensive word for the penis, be it in the context of humans or animals.
But as Orwell said, some animals are more equal.
"Ha egy hangyafasznyit is figyelnél..." ("If you paid just an antcockful of attention...")
"Ez kutyafasza volt ahhoz képest..." -> "This was dog's penis compared to..."
But there's more.
And still, we often use it similarly to "kutyafasza" because... probably unfounded machismo.
Or we can consider "lófaszjóska" ("Horse Dick Joe"), the archetypal useless layabout nobody.
It's the Swiss army knife of sweariness.
(Who's also a good candidate for a round of "Spot the Magyar", with his suspiciously Hungarian family name.)