This happens to me quite often but if I think a bit about it, I'm not 100% sure either why they're completely wrong.

If you want to get into the conversation (not recommended as it gets ugly quite often when people are completely sure of something * caugh...republicans... caugh*) it's actually better to argue on why they're wrong to be COMPLETELY sure rather than argue the opposite point you might think is right.

They will have far less argument to explain why their point is completely right than to show that yours isn't right either.