Horseshoe theory implies (if not explies, if that's a word) that going far left or far right automatically entails becoming authoritarian, and that they converge as you go farther "left" or "right". That's pretty demonstrably false, and even a two-dimensional political compass (let alone one with more axes) does a much better job of describing actual political stances than a horseshoe can. Authoritarianism v. libertarianism and socialism v. capitalism are separate and independent axes, and societies have existed across the whole gamut, corner-to-corner-to-corner-to-corner and everything in between.

I always viewed it as descriptive and not prescriptive, so I wouldn't say it implies movement across the authoritarian axis just by moving more right or left.

I feel like even as a descriptive theory it doesn't really map all that well to reality, though.