A "nuke" is simply slang for "nuclear weapon", and the US deployed two in WW2. It sounds like you might be talking about fusion weapons, which have certainly been tested but never used in anger; these are, in effect, just bigger bombs. No one bomb that humans possess can wipe out the species, or even make a dent. Nor is it a given that a single nuclear attack will lead to nuclear war.

As to why no one's used nuclear weapons since WW2, it turns out they're not hugely useful weapons outside of a "total war" context. Too blunt an instrument; rarely do you wish to simply wipe out a few square miles and everything in it.

I predict the first use, if it happens, will be naval.