this is a good question.
my initial answer:
no, the concepts behind anarchy (even anarchism) are relatively simple, even to me (a simpleton). one might say they are a (not the, but a) "natural" way of being and relating in the world.
however, what makes anarchy complicated where the rubber meets the road - living our lives - are the multitude and magnitude of indoctrinations and ideologies that the world we currently inhabit imposes upon us, from the moment of our conception/birth. all (or most) of which are intended to ingrain in us principles and desires that are completely contrary to anarchy.
so, we have this kind of innate sense of wanting to be free, yet we are constantly told that we should want something else; authorities, social contracts, law and order, etc. and of course, those things are imposed on us regardless.
add to that what human mentioned above: the different flavors and ideological leanings of anarchism, and the tendency for those talking/writing about it to be overly verbose, intellectual, and reliant on historical writings (which adds yet another level of mediation due to language and style differences between timeframes).
then, yeah, i can easily understand how one might see it as complicated.
in general, i think people tend to complicate things rather than simplify them. and when it comes to communicating ideas, i wish people would more often aim for conciseness and simplicity, rather than verbosity and complexity. and i know that ain't always easy. especially for those that attended the academy.