Here's why. The 'top' of the slippery slope is a point that reasonable persons agree is more or less reasonably acceptable. And the first few steps down the slope also seem somewhat reasonable to reasonable people. And the 'bottom' of the slope is where people agree that things have gone too far. And the argument asks "Where does the madness end? How do we stop ourselves, or know when to stop?
We know when to stop because, as the slippery slope presumes, we are reasonable people who recognize that the top is OK and the bottom is bad and this means we ought to stop somewhere in the middle. Reasonable people who are capable of discussing the pros and cons of where that point ought to be. Reasonable people who are not bound to "follow the argument to its logical conclusion" because we recognize that its conclusion isn't reasonable and that happiness is found in moderation. The slippery slope bothers me because it abandons common sense or reasonable moderation and turns complex issues into oversimplified, black-and-white, all-or-nothing propositions. It pretends that there can be no line if none exists rather than inviting us to discuss where to draw that line. It pretends that moral value judgments are some sort of death pact that must be followed to the grisly end rather than ethical guidelines that inform a series of open choices.
And it fails because of itself. If we allow slippery slopes to dictate our morality and actions where does the madness end? Will I be not allowed to marry a twenty year old because I might want to marry a ten year old? Will I not be allowed to drive 50mph because then I might want to drive 150mph? Should I not be allowed to eat veal because then I might want to eat human children? Of course not. Because we are reasonable people, and we shouldn't use the lack of an exact answer to set the limit at an unreasonable extreme.
Of course there are some people who genuinely don't seem to understand that there's a difference between a zygote and a four year old child, or a rifle and a nuclear bomb, or an adult human partner and a duck. It's fair to ask how to explain the difference to one of those people, especially if you are one of those people. And of course some people will not agree on where exactly the line ought to be drawn - reasonable people can disagree. And of course some people aren't reasonable, and will try to get away with things they know they shouldn't. And of course what some slippery slope arguers are really trying to say between the lines is that some issues can be complex with vague, arbitrary, and subjective edge conditions. And that's true. People are complicated. Life is complex and pragmatic moral choices are difficult. It's important to approach problem-solving and compromise-brokering with that understanding - so that you don't turn the result into a black and white issue. And that's why you shouldn't take the slippery slope cop-out seriously.
Caveat: A "slippery slope" is where things are OK at the top of the slope but get slippery on the way down. Trying to say that everything in a category is bad because some of the things in that category are bad is conflation, which is a lame argument for different reasons.