Closed doors are just a puzzle put on earth to keep cats entertained trying to open them, I'm sure of it.
Radar used to be drawn to the cupboard under the sink because we kept plastic bags there and his favourite thing in the whole world is shredding plastic bags.
Obviously we didn't want him doing that, but there are magnets on the doors and we thought that would be fine. Until one day Nate left the cutlery drawer open about 3" and Radar went missing and we found him about half an hour later in the forbidden cupboard peering out from behind the plastic bags looking very smug, having climbed (or I should say squeezed and contorted himself) through the slightly open drawer.
So after that we always made sure the drawer was closed. But then he worked out that he could open the door by lying on his back and pulling the bottom of the door with his paws.
So after that, we put a hair tie around the handles of the cupboards to hold them shut. He chewed through the hair tie in about 2 seconds flat.
So after that, I left a big bag of dry food propped in front of the doors. He somehow managed to push it out of the way.
We finally solved the problem by getting rid of all the plastic shopping bags, and putting the roll of bin liners in a top cupboard. Or so we thought. He can get the bin liners out of the top cupboard too. It's back to square one