Why do animated characters smile when they get hurt?

Answer 1

It's entirely up to the designer or animator what expression is used

Most of the time I would assume the animator had limited resources to work with and could not get the rest of the face to animate into the grimace required

Real people tend to grit their teeth and pull back their lips in almost a snarl from pain; the largest visual differentation between a smile and a grimace being the rest of the face and eye contorting from the pain rather than relaxing from the smile

With animation, getting everything around the mouth movement to change is not as symbol as it sounds, there are a million tiny calculations that go into it. Sometimes the best they can do is animate the mouth and without the rest of the face to contribute to the look, most emotions appear as smiles if only the mouth is being animated

Would add that if the purpose of the animation is to amuse and bring humor, the smile in the face of pain is comic detachment from reality. Making the drawn character more distant from real humans, and giving the the freedom to react in a totally unexpected way. Reacting in an unexpected way is very creative, and animators have many ways to move that unexpected way towards the humorous.