Your story is so full of stuff that can't be true, if there is no lease. If you never signed a lease at the start, you are month to month. If he asked you two months later to sign a lease and you refused, you are still month to month.
When you are month to month, it means he doesn't have to evict you. He can simply give you the state-required advance notice to vacate, and that's it. He doesn't need a reason. Paying rent on time means nothing. Getting a letter that says your cat is an ESA means nothing. If gives you 30 days notice to vacate in a 30-day state, you vacate. If you don't, then you can be evicted.
So something else is going on here.