There can be a signficant difference between the kinds of problems our friends help us with and and the kinds of problems that shrinks have unique information to help us with.
For example, I have a friend who has just turned 40, is still a virgin and is consulting a psychiatrist to decide whether to lose his virginity to a prostitute. I have given him my take on it which basically boils down to "get laid by whatever means necessary" but he is taking a more empirical approach and wants the advice of an expert on all of the possible psychological ramifications of his act before the fact.
Am I delinquent as a friend because I don't have enough information to answer his question? No. I'm not trained in psychology although I can give him some of my guesses about possible psychological ramifications - excitement, anxiety, guilt, wanting to go back for more.
However, because of his empirical leanings, his question is best answered by a professional. But to say that all he is looking for is "sympathy" would be a gross misunderstanding of the valuable role that a therapist can play because of his/her unique traning. My friend wants facts backed up by studies and he doesn't have the time or training to find those answers efficiently himself.
So to talk about 'mental illness' and 'sympathy' as being the primary distinguishing features of psychiatry vs friendship is a gross oversimplication of both.