I am more so arguing that in the pursuit of not tolerating the intolerant, we just end up becoming intolerant ourselves

Intolerance of intolerance is not the same thing as intolerance of tolerance. The former stops when other forms of intolerance no longer exist; the latter stops when tolerance no longer exists.

But more specifically, defining and understanding what constitutes intolerance is a non-trivial challenge that is often ignored. Oftentimes, a person or view is labelled as intolerant when it does not see itself that way. Oftentimes, the reality is more nuanced.

All we can do is give it our best try. It's better than doing nothing at all out of fear that we can't get everything perfectly right all the time. Intolerance definitionally seeks to destroy tolerance; thus it follows that if we do nothing, tolerance will be entirely lost.

You can see this kind of discourse online all the time. You go to a left leaning forum and find them calling the other side fascists. You go to a right leaning forum and find them calling the other side fascists as well.

The good news is that you don't have to simply take people at their word when they say things. Humans have the unique capacity for judgement.

I'm trying to demonstrate that the paradox of tolerance isn't actually helpful when it comes to decreasing intolerance.

I don't agree, but even so, you haven't proposed an alternative yet.