Shouldn’t an anarchist lean to the right?

I was looking at r/anarchism and there are only socialists and communists there, but doesn’t socialism defend a strong state that controls the entire economy and the people? So, I didn’t understand, because anarchism defends the extinction of the state, and the closest thing we have to that would be ultra-libertarian ideas, since the extinction of the state is almost impossible and there must be some body that guarantees the safety of the people.