(Assuming we are discussing neural pain rather than emotional...)

Pain itself is not normally bad; it is an indicator that something bad is happening, or will happen if you don't take corrective action.

So why do we think of pain as bad?

First , we tend to think associatively; because pain is associated with bad things, we tend to think of it as bad even when it is actually helping us.

More to the point, though, sometimes the pain itself is the problem. When there is no corrective action we can take, then the pain itself becomes bad because there is no reason for it; we have been alerted that there is a problem, thanks, but the unpleasant reminder continues -- like an alarm clock that refuses to shut off; it is evil and you want to smash it.

Our brains are wired in such a way that the sensation of pain itself is unpleasant; we may choose to do unpleasant things in expectation of some reward, but when an unpleasant thing is forced, that pretty squarely puts it in the "bad" category, I should think. (I would suggest that this is perhaps a good definition of suffering: unpleasantness you can't stop.)