The fasces was originally a symbol of Roman imperial authority and power. I’m not sure how it ever could have been a socialist or progressive symbol.

(Yes, I know the interpretation about the bundle of rods being stronger together - fascism is a collectivist ideology, just one with a distinctly narrowed definition of the collective - but trying to apply it to socialism just because it has collectivist themes ignores a) the history of the symbol, and b) THE BLOODY GREAT AXE IN THE MIDDLE KEEPING EVERYONE ELSE IN LINE).

Actually, the fasces predates the Imperial era of Rome, and is, indeed, less important and prominent in the Imperial era. The fasces is most strongly associated with the Republican era of Rome, when it was a symbol of magisterial power and authority, as opposed to arbitrary, personal, or royal authority (though it originates in the monarchy, there's a long, LONG discussion that can be had there about the Roman monarchy and its unique attributes that would be a very winding aside, so let's skip it for now). The bundling of the sticks represents the strength of the collective in imbuing power on the magistrate; the axe represents the power of life and death granted to magistrates by the people.

Obviously this is a bit more stark than symbols we prefer in the modern day - and rightly so. In the modern day, we don't need to be reminded that authorities are granted power over us by our consent; we need to be reminded that the authorities are granted power over us by our consent. But the origins of it are very much republican and, while I would hesitate to say explicitly democratic, considering the structure of the Roman Republic, more democratic than authoritarian.

Funny enough, the sticks were the more prominent symbol of keeping people in line. The axe was used only for executions, which would have been exceptionally rare (the first execution with the fasces' axe being used on those literally conspiring to restore the monarchy), while the sticks were used for corporal punishment, both subject to an appeal to the people before punishment.

For that reason, the fasces was widely used in republican movements in the 18th and 19th centuries, back when everyone was a Romaboo, and only rarely in monarchial movements outside of throwbacks like Napoleon.