Most people are idiots. You can easily prove this because they will agree with the claim in the title. If you try to give them a counterexample — like, you know, the vast majority of smokers not having cancer — they will counter it by "well, it doesn't cause cancer right away". Causality doesn't work like that; it's a "if X, then Y" relationship. Don't use the word if you mean something other than that; say "smoking increases the probability of getting cancer" (yes it does).
As an additional counterexample to the claim, here's something most people will disagree with: passing under a ladder brings bad luck. Mark Twain had a humorous take on this: a character tells another "X passed under a ladder and only six months later he fell and broke his arm" (I'm quoting from memory). That's exactly the same type of "causality" as in the case of smoking: you do X, then long after that bad thing Y happens, and you claim Y is caused by X. This is pure superstition; most people know that in the case of the ladder, but not in the case of smoking.
As for why: as usual, it's because of religion. Most people, as I said, are idiots and they prefer not to think; being told what to think is easier for them. Since the high priests of the current reigning religion of the world (aka science) tell them that walking under ladders does not cause bad luck, they accept it; when the priests tell them that smoking does cause cancer, they accept that too.
As I have mentioned before, I have lost my faith in education as a weapon against this kind of stupidity. People today are infinitely more educated than those living a hundred years ago and they still have the same lack of desire to challenge their own opinions (Paul Graham has a great article about this). This conflicts with my powerful belief that humanity always improves socially long-term (we're better now than a hundred years ago and so on), so that's a contradiction I haven't solved yet.
Oh well; end of rant. As the non-A adepts say, be precise; if you believe that smoking is bad because it negatively affects one's health, say that; saying "smoking kills" is more emotional but also incredibly stupid.