I first encountered this political theory in jr high or high school via a couple teachers who had progressive/liberal politics, but liked to think of themselves as more radical than they actually were.
In describing things like the tendencies of fascism and state communism to centralize and have authoritarian structures it makes some sense, but I don't think it is more accurate than some other more recent models I have seen in charting that, for example, the Political Compass (http://www.politicalcompass.org/
) and in some ways I think it is far less nuanced.
However I don't think either of these theories actually is very helpful when talking about anarchists. The political compass maps a position based on the presumption of state, government, etc. So, for example, I just started taking the test and quit after about 12 questions because I didn't find my perspective represented in the possible answers> Depending on how I chose to engage with that lack of options, I have previously been categorized as both left and right libertarian by the test. As far as the horseshoe theory, it tends to also leave out huge swaths of what define anarchist and anti-state politics (never mind anti-politics).
I think probably the most honest thing I ever heard about the horseshoe theory was when, trying to wrap my head around where an anarchist would fit in it, I asked the teacher of my high school civics class that very question and she looked at me and said, "anarchists aren't even on this chart." twenty years on, that has proven to be the most true thing I took from that class.
(edited for some readability issues)