....

[quote]Do they have a bias? Would I have more chances of being accepted if I lied and said I wanted to teach law? What proof would I need for them to believe I want to?[/quote]

No.

And didn't you already ask once and have your question answered? (https://llm-guide.com/board/general-forum/how-to-demonstrate-commitment-to-teaching-214773)

I'm also not sure indicating you are prepared to lie reflects well on you.