Oh, lordy, he sounds like a one-man entitlement festival. I feel for you.
You know. You
should tell him that there's no "our" in the equation, because it's not like you have some kind of commitment to him - like a long-term relationship or a marriage. So, it's
well within your rights to tell him not to assert ownership over things that aren't his. ( It shows how entitled he is, if he feels like your cat is also
his cat - I mean, wtf.

)
If you're non-confrontational - well, you're going to have to learn to be less so. It might help to look in between his eyes instead of right at him (it gives the
illusion of looking at his eyes.).
And eventually, move into another living situation. 5 dollars says that he'll try to stop you from moving away from him, so stand firm.
(Seriously, the whole "our" thing sounds very strange to me. I don't know him, but if I were forced to analyze him, I'd say he's trying to dominate you.)
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