Just accept it and life will become easier.

If you're a guy then I get it. Male cat owners always seem to bow down to the wishes of their Cat Overlord. That same cat will not even bother trying to pull those stunts with a woman. At least, that's been my experience. When he had to go out of town, my ex used to tell me exactly how and what I was to feed the cat, and to expect to have to go out and call her several dozen times from sunset to midnight, before I'd have any hope of getting her inside. Well, I fed her what I decided to feed her, she ate the lot, and came in as soon as I called her. A cat soon learns who it can walk over, and who won't stand for any nonsense.

There is a 1960s Sci-Fi Novel by Robert Heinlein called "The Door Into Summer". In it the protagonist has a cat, and lives in a house with 11 doors leading outside. During the winter he had to open all 11 doors for the cat because it was sure that one of those doors would lead outside to Summertime. Be glad you only have 2 doors.

Mine does the exact same thing. Do weird..

Anyone who owns a cat is a slave to a cat :p

Cat's aren't aware that two different entries can lead to the same area. That's why they might come in one door, and insist on going back out the other one, because it's a different outside and they have to check both of them

Cats shouldn't be out door cats. It's dangerous and they poop and spray in your neighbours yards. Your neighbours probably don't like your outdoor cat. Dumbass.

Cats have caretakers, not owners

You want stubborn one time the cat I had growing up insisted on coming in the back door didn't matter if my mom called or my dad the problem with coming in the back door was the steps were being replaced an it was about 4 feet from the ground to the door I think the cat wanted to be picked up an brought in but after a lot of encouragement from me an my sister our cat finally made the jump

I read somewhere recently that cats do this because they don't understand that it's the same outside through both doors. Or that it remains the same outside even if the door shuts and is reopened.