It's as "bad" as using "dick", which you wouldn't give two shits about. In fact, you yourself recently used "dicking around", which I guess should be, by your own logic, not okay. Right? After all it's about wasting time, so it has negative connotations, which you're applying to the male sex.
Also, he's from Australia. Stop bringing your stupid US crap into everything please.
The problem isn't that it's crude and refers to sex organs. The problem is that it's misogynistic. When someone says "cunt" or "pussy" or "bitch", they are saying "You are acting like a woman, and being a woman is bad."
"Crying like a bitch" does not refer to women at all, it refers to a female dog. The full phrase is "crying like a bitch in heat" and refers to the whining female dogs do when they're in heat.