I think if a dislike button were introduced it would be used in bullying - sadly there are a few groups of dramatic people on here who target specific users.
It would also prevent debate. The internet already throws up a lot of barriers to debate as it's easy to dehumanise the person you're speaking to, if we give people a 'hate' button that's another way to make something that SHOULD be complicated into a simple yes/no system. You could argue that the 'like' option is the same, but I don't think the internet is known for causing people to get on better. One has a measurable negative outcome, the other doesn't.
In favour of the dislike button, there was a post today attacking women, and the poster deleted every comment disagreeing with his worldview. You can argue that a dislike button would give users the power to vote this down and not have their views deleted. But who does this benefit? It just means the creator of the hate post feels attacked and vilified. At least when he's deleting arguments against his world view he can read them first. Just getting a straight up 'dislike' actually just proves to them that they're right, and everyone against them - but without explaining the reasons to them.
Ramble over. I think.