What's bad faith about my argument? There's only two options: You believe what you typed and that it's impossible to make this mistake, or that you were using hyperbole, and you acknowledge that it is possible to make this mistake. These two options are both mutually exclusive and binary-- there can be no other stances. (and notably you haven't actually clarified which one you believe.)

I didn't make you choose to defend a poorly thought out stance. That's on you.