Most mythologies that I read are used to justify the power structures in society.
Are there any that instead preach democracy, anti-authority, pro-education, or free love?
If memory serves, Mikhail Bakunin was particularly fond of the story of Prometheus, the Titan of forethought. Prometheus defied the Olympians (the ruling class), stole fire from Zeus (the king) and gifted it to humanity. It does not get any more anti-authority than that!
Here's one version of the myth, from Hesiod's Works and Days:
For the gods keep hidden from men the means of life. Else you would easily do work enough in a day to supply you for a full year even without working; soon would you put away your rudder over the smoke, and the fields worked by ox and sturdy mule would run to waste. But Zeus in the anger of his heart hid it, because Prometheus the crafty deceived him; therefore he planned sorrow and mischief against men. He hid fire; but that the noble son of Iapetus stole again for men from Zeus the counsellor in a hollow fennel-stalk, so that Zeus who delights in thunder did not see it. But afterwards Zeus who gathers the clouds said to him in anger: “Son of Iapetus, surpassing all in cunning, you are glad that you have outwitted me and stolen fire—a great plague to you yourself and to men that shall be. But I will give men as the price for fire an evil thing in which they may all be glad of heart while they embrace their own destruction.”
Hesiod. The Homeric Hymns and Homerica with an English Translation by Hugh G. Evelyn-White. Works and Days. Cambridge, MA.,Harvard University Press; London, William Heinemann Ltd. 1914.
The "evil thing" Zeus gave men was Pandora's jar, a jar that contained every evil there is (but also hope). Prometheus was also severely punished. Zeus bound him on a rock and had an eagle feed on his liver. The Titan's liver would grow back overnight1 to be eaten again the next day. The hero Heracles eventually saves Prometheus when he comes across him on his way to steal the apples of the Hesperides.
1 Interestingly, this might suggest that the ancient Greeks were aware of the liver's regenerative abilities.
An anarchist message can be found in Antigone's refusal to abide by King Creon's decree to leave her brother unburied, as dramatized in the play "Seven Against Thebes" by Aeschylus.
Interestingly, the first known use of the word "anarchy" in a political context is in line 1035 of the play.