"emergency" rather definitionally indicates that "not normal" or "out of the ordinary" situations are occurring. For most callers, this may be the worst day of their lives - emotion/stress/danger/death/etc.

They're not required to interpret a caller's phone voice as 'hostile' either. Unless the caller actually says something like "I'm going to come find you and kill you or your family" or something along those lines, I don't think there's any reason anything a caller says should be interpreted as 'hostile' to the dispatcher. If they're agitated/upset - well... they're having an emergency.

Should medical staff not expect "sick people" in their office/hospital?

Someone who can't handle someone yelling or swearing on the phone should't be in a dispatcher role, and... yeah, I think it's gotta be stressful for them too, and they probably shouldn't do it a whole lot, as they'll burn out quickly.