Thought crime = hate crime?

I was reading about Bishop Richard Williamson on wikipedia as a result of reading some article where the pope had said something stupid about condoms, Africa and HIV/AIDS. Anyway, this bishop, it turns out that he denies that the holocaust ever happened. Not only does he hold that view, but he's said so in public interviews. According to his wikipedia article, holocaust denial is illegal in Germany. I found this to be incredibly strange. Why should it be illegal? Personally, I think that the holocaust happened. There is no doubt in my mind that it happened, nor that it was a terrible thing, but I don't think that it should be illegal to think that it didn't happen.

Why should it be illegal to have this belief, when it is not illegal to hold any other belief (in most civilized countries anyway)? If we take the holocaust for a provable certainty, as we should, then we can compare this disbelief to the disbelief of any other provable fact. For instance, if I held the belief that 2 + 2 actually equaled 5, should I be labeled a criminal? Clearly these two issues do not carry the same emotional charge, but they are both opinions, after all. This, I believe, falls squarely under freedom of opinion and speech. It's not illegal to be a Nazi (hold the belief that national-socialism is the way to go), to take something related, so why should it be illegal to hold this particular belief?

This isn't about this bishop. People should be allowed to think what they want without being labeled criminals. Maybe there is more to this particular illegality than what I have discovered, and if so, I would very much like it to hear your opinions about it.