“Left” doesn’t mean socialism. In the long run, it comes out of the enlightenment period, quite literally.
Traditionally, the left is associated with small “L” liberalism, and the right is associated with small “C” conservatism.
Generally speaking, it has been a historic debate between whether the “natural” way things are is good and prudent (e.g., monarchs, religion, castes, roles, and norms), or if the way things are should be challenged to try something that seems better (e.g., liberté, égalité, fraternité).
When one of these ideas is successfully, it is often adopted by the right, when one fails, it is often abandoned by the left. Whether or not socialism is part of the left depends on whether folks on the left think it’s an idea worth trying. In America, right now, the vast majority are still quite hesitant to include it in their platform.
> “Left” doesn’t mean socialism.
In American english it does.
> when one fails, it is often abandoned by the left
Rent control has never worked out (it results in a housing shortage), but proposals for more rent control constantly flow from the left.
It's confusing because different people mean different things when using political terms. The political compass (https://www.politicalcompass.org) has two axes: left-right and libertarian-authoritarian. On it, socialists are definitely left wing (and communists far left), regardless of what the left/right wing meant at the time of the French Revolution.