I think Eliezer’s using these terms in a more specific sense than you are. For instance, your Person 2 is making an appeal to egalitarianism (in the conventional sense) as an argument for their position; while it still may be invalid, it’s not an argument for why the debate should stop, which is what this post is about, if I’m reading it correctly. The appeal to egalitarianism is something like “Both of us have equally valid opinions, so who’s to say which of us is right or wrong? Let’s agree to disagree.” The appeal to personal freedom is “I have a right to my opinion, so by arguing with me, you’re infringing on my rights” (I encounter that one depressingly often), “I define my words this one way, so by disputing that, you’re infringing on my rights”, etc. They’re never arguments (even wrong ones) about the actual merit of the views being debated.
I think Eliezer’s using these terms in a more specific sense than you are. For instance, your Person 2 is making an appeal to egalitarianism (in the conventional sense) as an argument for their position; while it still may be invalid, it’s not an argument for why the debate should stop, which is what this post is about, if I’m reading it correctly. The appeal to egalitarianism is something like “Both of us have equally valid opinions, so who’s to say which of us is right or wrong? Let’s agree to disagree.” The appeal to personal freedom is “I have a right to my opinion, so by arguing with me, you’re infringing on my rights” (I encounter that one depressingly often), “I define my words this one way, so by disputing that, you’re infringing on my rights”, etc. They’re never arguments (even wrong ones) about the actual merit of the views being debated.
Oops, yes, I misread the original post. Thanks for pointing that out.