I'm different, had cats and other pets all my life and have 2 cats now and yes I have rehomed two pet before.
First was given to me and HATED me from day one, I have NEVER clashed with an animal like that before or since. It was miserable and turning violent, I was miserable and sick of being attacked, I literally couldn't afford the damage it was causing and it kept escaping (it would literally chew threw walls, fences, destroyed the house and everything, couldn't be calmed or contained. frankly if it was a dog it would have been put down under the danger act). It was no life for either of us. I stuck it out for a year (far too long with hindsight) then saw someone else want that specific pedigree bread (they had had several before, they where experienced in the diva temperament and for some inexplicable reason it didn't attack them like everyone else) popped up and not going to lie was not sad as they drove off with him.
The other I genuinely loved, one of the most wonderful pet I ever had and was a shining light in one of the darkest part of of my life. I was homeless and struggling to look after them so gave them up. It was sad and I lost the only thing I had at that time in my life and was left alone.
People are like a pet is forever you cannot EVER give them away... no a responsible owner does whats best for the ANIMAL which can often be re-homing.
Most people considering rehoming are struggling to cope which means animal care will suffer. It's FAR better to re-home somewhere more suitable before neglect becomes and issue (in which the animal will be taken and end up in a shelter later) and the animal suffers.
People rehome because they can't physically, mentally or emotionally cope anymore and thats fine, you are allowed to have health problems and life changes. There are over 83,000 CHILDREN in care (some remove some voluntarily surrendered) due to these issues effecting the parents ability to care so why people think pets don't end up the same is insane.
Also shelters have nothing to do with it if you are responsible, I have never given an animal to a shelter nor gotten one from a shelter. Shelters are where animals that weren't carefully re-homed when they needed to be end up when its far too late.