This is the kind of explanation that doesn't explain anything to the people who need it explained.
If it helps, consider horseshoe theory as the idea that all authoritarian systems start doing similar things, completely independent of economic models.
It's still not great, but at least there's an observation in there.
You can start a separate conversation on whether there's any value to conceptualizing a left/right spectrum at all (there isn't)
Yes, someone that knows what words means knows that, but the people that unironically talk about horseshoe theory don't, so all they see is someone who clearly doesn't understand that "Them commies love dictators"
Because explaining exactly why it's nonsense, even if you can point to certain "socialist dictators," can be a good opening into deprogramming a liberal that can't define liberal.
Just to flip this, do you have any sources that horseshoe theory is a real thing? That's the funny thing about language, someone put Theory in the name and now people think it's a real thing.
To save you the trouble, it hasn't held up under academic study. Plenty of info on Wikipedia about it.