Slippery slope is not a fallacy. It's a real phenomenon in certain cases. It does, however, have to be proved relevant to any given question, which is GP's real offense.
Yes, this is why it's a fallacy. By the time you've justified a slippery slope argument, you have made an independent argument for your point that has nothing to do with the idea of a "slippery slope". Calling something a slippery slope without an additional complete argument is the slippery slope fallacy.
> ...you have made an independent argument for your point that has nothing to do with the idea of a "slippery slope".
Um, no, it probably does. Slippery slopes happen when there's unintended consequences embedded in the assumptions behind a proposition someone is putting forward, and there are people with an interest in pushing for them to be realized. Sometimes you talk about this in your argument; bam, slippery slope argument.
To try to name a "fallacy" after this rather useful concept, when the "fallacy" is just the boring case of failing to make an argument at all, is useless confusion at best.