Positive means you found the special thing you are looking for; negative means you just found an ordinary thing. False positive means you thought you found the special thing but you didn't, it was just ordinary; false negative means you thought you found an ordinary thing but actually it was special.

False positives mean you throw away ham as spam (terrible), false negatives mean you let some spam into your mailbox (not a big deal). But false positives also mean you diagnose benign as malignant (annoying), and false negatives also mean you diagnose malignant as benign (fatal).

So depending on what you are looking for, it varies whether false negatives or false positives are worse. Or maybe they can be equally bad.

I don't think you need to rename positive and negative as long as positive is understood as unusual and negative is understood as normal.

But spam is more "usual" than ham, so ...

Hmmm, good point. Ok, if you count individual messages, there is more spam, but if you look at the kinds of spam messages, they are way less diverse. So spam goes into one of ~10 buckets (419, pharmacy, fake conferences, view my profile, etc.), but the rest goes into 1000 different buckets. But you still have a good point.