Equality of opportunity is not the same thing as equality of power.
Equality of opportunity means we all have the same opportunity to attain positions of power. It means that we each have the option of climbing the greasy pole of structural authority. It means that in theory there’s nothing stopping you, me, or anyone else from becoming the ruling tyrant.
That’s why equality of opportunity is not consistent with anarchism.
Equality of power means that there are no positions of power, no structural authority, and no potential to become the ruling tyrant.