The underlying assumption behind free speech, free assembly, the public sphere, democratic assembly, etc. is that some ideas are better than others, that people can argue about these ideas and determine which ones are better, that other people will be convinced by rational argument, and that society is better when the better ideas win.

I don't think this is quite what you're saying, but "Why is your definition better than mine" reminds me of a lot of discourse I see about free speech, where free speech is an inherent virtue, and you should be able to say whatever you want to say without anyone doing anything about it - neither censoring it, nor objecting to it, nor listening to it with a critical ear or responding with anything other than "Yay, speech."

This seems to me to be the most fatal form of censorship. We're essentially sandboxing speech. Say whatever you like, as long as it doesn't actually mean anything. Participate in public debate, as long as it doesn't change. Respond to others, as long as you don't dare to claim that any idea might be wrong. What is the point of free speech in such a society?

If all ideas are equally valid, or at least the ideas of the inside crowd are valid and outsiders get a "who are you" response, why do we even try to have a democratic society? Just let the king do what the king wants, or the CEO do what the CEO wants. Comment and criticize all you want, as long as it doesn't have an effect.

But if we believe in there being a point to free speech, we should respond to speech with "Why do you believe that, and can you try to convince me that I am wrong while I try to convince you that you are wrong" instead of "Who are you to disagree with me".