You may have overlooked smth: Caring for others' well-being is also a kind of hobby. See a doctor's smiling face after curing people without requiring anything in return? Can you say they are not happy with what they have done? Can you say they hate it?
Technically speaking, if anyone does anything that's purely because they want to do it, they gain nothing in return, it's because it's their hobby. Whether it is killing or saving people, it's the same category when you look at it this way. It just so happens that the will of the "selfless doctor" aligns with people, aside from that, not much difference.
Don't get me wrong, I probably like the doctor better than the killer, but from a fair point of view, they are not that much different as a person who just doing what they like.
In case you ask, I would like to give you an example: A killer will be executed or jailed in a normal society, but they could also be admired and loved as idols by many others (killer or pervert). Or that doctor could be hated for ruining other's doctor's money income.
Every coin has 2 sides, but by removing those sides, you can see it is in the end, the coin. The doctor or a killer too, essentially the same.
And yes, I do mean the serial killer, because I want to refer to someone who kills people just because they want to kill to compare with the one saving people just because they want to save them. And by the doctor, I mean the "selfless doctor".