Slippery slope arguments falsely assume that one thing must lead to another. They begin by suggesting that if we do one thing then that will lead to another, and before we know it we’ll be doing something that we don’t want to do. They conclude that we therefore shouldn’t do the first thing. The problem with these arguments is that it is possible to do the first thing that they mention without going on to do the other things; restraint is possible.
Example
(1) If you buy a Green Day album, then next you’ll be buying Buzzcocks albums, and before you know it you’ll be a punk with green hair and everything.
(2) You don’t want to become a punk.
Therefore:
(3) You shouldn’t buy a Green Day album.
This argument commits the slippery slope fallacy because it is perfectly possible to buy a Green Day album without going on to become a punk; we could buy the album and then stop there. The conclusion therefore hasn’t been proven, because the argument’s first premise is false.