Both my cats came from an well-run rescue place. One where the animals didn't live in cages all the time, but was only open on weekends when the "foster parents" would bring them in for a few hours to meet prospective adopters in a huge window-walled playroom filled with toys, cat furniture, and a couple human chairs.
My girlcattt had been "in the system" for 8.5 months, because she wouldn't approach ANYBODY. She didn't act scared or bite or hiss or anything, she just refused to interact, and people would pass on adopting her. After 20 minutes or so of being pointedly ignored, they'd say, "Sorry, not this one. Who's next?"
When I showed up the first time it was to get a BFOC. (Big Friendly Orange Cat) The rescue people always craftily ask if you'd like to familiarize yourself with how things worked by meeting a couple NON-candidate cats first. (Meaning, in my case, not a BFOC.)
Why? I learned afterward it was with the hope of having happen exactly what DID happen. The "familiarize yourself with how things worked" cats were always the hard cases that no one had adopted, you see...
And the alternately regal and goofy little raccoon-colored girl cat they brought in---the one nobody had wanted in 8.5 months and was a near polar opposite of a BFOC---was instantly my best friend for life. She was all over me in the best possible way and after playing for a solid half hour decided to take a nap on my shoulder.
The staff of the adoption place literally lined up outside along the clear wall to see it for themselves, and one of them was openly crying.
CATS CHOOSE THEIR HUMANS
Been there, done that, seen it.
Twice
Because three months later when I decided girlcattt needed a playmate/friend, the exact same thing happened again.
A big, gawky, ginger boycattt that had ignored every human he'd been put into the playroom with for 3.5 months jumped straight into my lap and stayed there like I was a magnet. For fun (again the staff was at the window), I'd set him on the floor and he'd jump right back up. This went on for half an hour. His choice was made, and that was that. It was equal parts amazing and slightly sad to think of all the time he'd spent alone, a hostage to his instincts, waiting for the right human to come along.