Anarchism is measured on a separate axis with authoritarianism at the top of the compass and libertarianism at the bottom. Anarcho-communism is in the bottom left quadrant because it is both libertarian and communist.

Just because anarcho-communism would like to abolish the state doesn't make it opposed to socialism. Anarcho-communism is in support of social ownership and democratic control, both of which are socialist nature.

The political compass was made as an alternative to the traditional left versus right spectrum that came about due to the French Revolution because a lot of people saw it as too simplistic.

I realize that the left at that time had nothing to do with socialism. However, we no longer live in 18th century France, and it is now common to put socialism on the left and capitalism on the right.

As for what I think fascism is, I agree with the commenter below me.