I'm an anarchist and also a giant nerd, so I actually have some context for what an anarcho-monarchist is. Firstly it's an ideology that most anarchists hold to be about as ridiculous and contradictory as you do, for fairly obvious reasons. It's probably got more claim to being an actual form of anarchism than fucking anarcho-capitalism though, which anarchists pretty much universally agree is not actually a form of anarchism. It's basically the idea that the monarch should exist as a divinely ordained religious and moral leader, like a sort of moral exemplar that society can aspire to, but without any of the hierarchical power structures of a normal monarchy. It's sort of a way to square anarchist tendencies and beliefs with the weird psychology of living in a culture where having a monarch is a big part of your national identity. It's kind of what J.R.R. Tolkien believed which is why he comes up in this discussion several times, because he developed a healthy distrust of authority by witnessing the horrors of the first World War, but was also very British to the point that he could not have straightforwardly good politics and so he ended up in a weird an kind of incoherent place.
I don't understand it either but I think some of the people who hold to it have their hearts in the right place, for what it's worth.
