Question: Few versus a few (or little versus a little etc)

I would have agreed with you. I googled and found something that said few (with no “a” before it) “could mean little to none.” Such as, he has few options. So maybe he is right but I feel most would agree with you for general use of the word.

It doesn't mean none.

I have few friends = I don't have very many friends.
I have a few friends = I have about three or four friends

 Your teacher is wrong. Few means a small number.

"Few" is not the same thing as "none". lol.  "I have few friends" means "I don't have very many friends". "I have no friends" means "I have no friends" . 

I agree with AussieMeg’s interpretation of the numbers, but I would also add that if I wanted to emphasize a negative feeling about how small my number of friends is, I would use ‘few’. If I wanted to emphasize it as a positive, in that I do have some, I would use ‘a few’. I think this one is more about context than the literal number.

I personally disagree with both your teacher and any internet source stating that "few" means "none".

I will say, however, that in some circumstances, people may use the word "few" when they don't want to admit to the reality being "none". So if I have no friends and I don't want to say that, I could say "I have very few friends." But to me, personally, I'd still consider that statement to be a lie if I did indeed have absolutely no friends. I'd say "very few" could mean one friend, but not none.

I always thought that few means - not many - as in 2 or 3 or 4.

If your teacher is not a native speaker, odds are the meaning to him is cultural. Technically, though, he's incorrect.

I’m not saying I agree with it, I’m saying I googled and found something else that supports what the professor said so it’s not completely out in left field. I stated I wouldn’t have thought that myself.