Socialism requires authority.
Else, who decides what is equal? Who ensures the proper distribution of benefits and entitlements?
You mistake Freedom with Libertarianism anyways.
We are not talking prefix here.
Socialism, in it's traditional and true definition, means "the workers democratic ownership and/or control of the means of production". Such a definition implies that rather than a government bureaucracy for managing such means, there is a focus on highly democratic organisation, education and awareness, and every individual is encouraged to become an active, rather than passive participant in that which effect their lives. Only the workers themselves bear the knowledge of what their own freedom and liberty means, and only they know what is best for themselves, ultimately. Advocates of the state, be they on the left, or the right, have repeatedly defined the meaning of "socialism" to mean arbitrary rule by a set of "leaders", or a political con-game in which socialism is no more than capitalism with a few token adjustments for bearability.
Call it phony universalism, Robin Hood in reverse, or socialism for the rich -- the United States spends almost as much helping the have-plenties as the have-nots.