It appears that the word sycophant originated during a war between
Athens and
Thebes.
The Athenians were avid figs consumers, and Thebes was one of the greatest fig exporters in Greece. Because of the war, a fig embargo was decreed and a florid theban figs black market was soon born and, with it, the much hated character who took it upon himself to inform about the illegal fig trade.
Because in ancient Greek the word for fig is "sukon" and "to reveal" translates as "phaino", the above mentioned character was called "sicophant" - one who reveals about the figs.
(The first time I heard about this etymology from my Greek teacher, she told that the second part of the word came from "phemi" - to say. 15 minutes into my E2 experience, my attention was called to the - much more sensible - derivation from phaino)