I think that Socrates certainly was a philosopher, particularly in the sense that he was lover of wisdom. One of the reasons I think that he had no teachings was that Athens in the midst and wake of the Peloponnesian War had been overrun with Sophists (the political consultants of the day) who all had ‘teaching’ they would sell to the whoever paid them. Since the Sophists viewed knowledge merely in instrumental terms for the wealth and power they could generate they and their students were not in a position to love truth and beauty, that is to be true philosophers. As Reeve and Miller remind us the Sophists and their ilk were arrogant because they though they had all the answers (Reeve Miller, pg 45). Socrates, however, as a true philosopher believed that philosophy, especially through the use of the Elenchus, had a moral aim which was to get people to realize that they really didn’t know what they thought they knew and a result they would be open to truth and beauty which would help them lead happy and virtuous lives. (Reeve & Miller, 45-46)
Reeve, C.D.C., and Patrick Lee Miller, eds. Introductory Readings in Ancient Greek and Roman Philosophy. Indianapolis, Indiana: Hackett, 2006.