Anarcho-capitalism as a phrase was basically Rothbard trolling. What ever merits it may have, it shouldn't be lumped in with the rest of anarchist philosophy.
(also to be clear I think ancap has approximately zero merit)
Anarcho capitalism is an oxymoron because capitalism is heavily based around centralization and inevitably leads to monopolies. Corporations are less democratic than the government and the competition argument doesn't work for monopolies.
Ancap is an oxymoron because it's predicated on strong abstract property rights, and you really need a fairly large government to enforce them. And if you take those away, you end up with something more like mutualism.
(also to be clear I think ancap has approximately zero merit)