The problem being, if they were already prone to spending concerted, honest effort in facing and talking about their problems, they would be a lot less likely to be in that place.
Sometimes a cigar is just a cigar.
If your behavior is outside of the social norms (eg. you leave dishes out for others to clean) then admit fault and move on. If they bring something else up maybe you are correct in your thesis but why are you defending yourself when you are being a slob?
If you think the behavior you described is just about a couple iced tea bottles, that is… not likely to go well long term in my experience. I hope I’m wrong for you though!
And the statement you’re making there seems to have a tone of resentment towards her which, unfortunately, is going to likely be a problem too.