While I do think belief is much more than simply being intellectual assent, I wouldn't characterize it as submission, although submission will attend one who exercises faith. Rather, I see it as a radical trust in what God has revealed. So I believe faith or belief is more robust than solely submission.
I don't think I ever mention the word submission.
Maybe I'm asking more than your willing to do?
See how he's trying to manipulate you? Make you feel inferior to him? Instill guilt that you aren't doing enough? Get you to only use the language and terms he wants you to use so that he can control the discussion and subsequently control your mind?