I mean you wanna be technical about it socialism is a much wider spectrum of ideas than Communism. There are definitely people who define it strictly by the presence of the worker co-op or as anti-capitalist but that’s one floating idea in a nebula. Market Socialism for instance is basically a blend of capitalism and socialism where things like capitalist incentives are still maintained but regulated and systems of social support are expanded to make up for the gap of the whole capitalist “not my monkey not my circus” washing of hands of social responsibility to be an active part of a community. It’s basically anti-capitalist in the same way putting up a privacy fence is anti-neighbor… So a wide spanning income based taxation could be construed as sort of Socialist but its basically the air we breathe as far as a norm goes.

But Harrison Bergeron is more like the Conservative satire of what “Cultural Marxism” looks like in practice. The strawman idea that is designed to make people clutch their individuality and random blessings like something someone wants to forcefully take away from them… It’s a metaphor for things like social programs and inequality conscious measures that lift up disadvantaged people to allow them access to participate in society but not a particularly good one as it pre-supposes that lifting someone up is the same thing as crushing persecution of the naturally gifted.

Your teacher was half right, the story is about Socialism but it’s a hostile framing of Socialism in complete bad faith using the conventions of science fiction to paint an overblown dystopia with hyperbolic absurd metaphors that underline the anxieties anti-civil rights advocates had when it was written.

The whole thing makes more sense when you consider that hardcore disability advocacy groups that started the path to creating the ADA basically was beginning to gain traction when the book was being written.