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Socialism is still capitalism. It’s just regulated and we use taxes to fund social programs.

Tell me you don't know the definition of socialism without telling me you don't know the definition of socialism.

While Socialism may not be against Free Markets, Capitalism /= Socialism.

Socialism is when the workers collectively own the means of production.

So like in a factory, everyone employed there also has ownership stake in the company, and they can vote on leadership internally. Instead of relying on government regulations to be able to have things like paid lunches and guaranteed sick days, instead they can come to collective agreement on those things, with the vote of every worker/owner. They can still sell products on a free market, but the "capital" part of the equation has been removed.

In capitalism, in a factory, the factory has been purchased by a Capitalist who, by definition, is someone with a lot of Capital (money/wealth) and they bought the factory whole with the capital. Now, they are going to hire workers with the capital as well, and the workers have to follow any and all their rules, like a little fiefdom of a dictatorship and nobody gets an opportunity to vote on leadership. They have no control over pay, working conditions, or much else, and they rely on the Government to enforce it otherwise.

Socialism really doesn't have anything to do with government regulation, taxation, or social safety nets.