It's the anti-establishment impulse taken to extremes. Anarchism is one of the niche destinations of that mindset. Another, ironically, is full blown communism.
What's sort of funny, is how all these seemingly polar-opposite anti-establishment flavors are actually far closer to each other than they are to mainstream political left or right.
The anti-establishment part ends up overriding everything else
That's how you end up with Bernie/Trump crossover voters
How is it ironic? Anarchists were a big part of the First International and left-anarchists can usually be considered to be socialists. They are not polar opposites, rather communism and (left-)anarchism are the statist and republican/federalist (loosely authoritarian and libertarian) expressions of the same underlying ideology of human equality.