The oxymoronic identity is libertarianism. It masquerades as anarchy but doesn't oppose capitalist oppression.
I see a pattern here - you're operating on a twisted set of definitions - this isn't the first time I'm seeing this when debating people online
Particularly, you have completly different definition of anarchy. You probably consider it some sort of organized social system, but I consider it lack of any framework being enforced.
If you don't understand the difference between these definitions, you can't have any dialogue.
With the definition I use (and many other people BTW), basically anarcho-anything is an oxymoron. When somone talks about anarcho-capitalism, it's nothing but gibberish to me.
In light of different definition, consider this:
Libertarianism has nothing to do with anarchy - it's a system that minimizes state intervention to the absolute minimum, leaving as much to free market forces as possible, providing only minimal legal rails for enforcement of agreements.
There's no paradox here if you run with that thought process.