**Neither a teacher nor a native speaker.**
As far as I know they have different meanings:
Few = You wish you had more.
A few = You don't have many, but they are enough.
I have a few friends. (I don't need or want more friends.)
I have few friends. (I hope I will have some new friends soon.)
So in your example:
1. There are a few doctors in town. - It's okay, no one should die when s/he's sick.
2. He had few reasons for his opinion. - He wishes he had have more, but there weren't more. -> So his opinion wasn't taken that seriously by others.
Student or Learner