Slippery slope is a
logical fallacy, and not a
rhetorical one. Logic and rhetoric follow different rules. Logic is purely binary - If I say "Burgers are unhealthy", and you can find one example that fits the definition of a hamburger that is made of plants and not full of fats, you have disproven my logic. Rhetorically, though, the point will stand as most burgers are "sometimes food".
One great way of thinking about it in modern terms is thus: Rhetoric is Bayesian. You're operating on probabilities. There's a ton of things that are likely to happen but not guaranteed. There's a ton of questions to which there is a large field of possibilities, and one action can cause opposite effects in different cases.
One of the best examples in modern times is "Appeal to authority:" This Doctor say X is true, therefore X must be true. Even large groups of doctors have gotten important things wrong[1]. Thus, a logical fallacy - X says Y is enough to create a predicate as the beginning of a chain of logic, but it is not "Proof" within a logical chain. "X says Y. X is a Doctor. Therefore Y" is fallacious logic. Nonetheless, you should listen to doctors, because rhetorically they probably know what they're talking about on medical issues.
[1]https://en.wikipedia.org/wiki/Ignaz_Semmelweis