Sometimes animals need to be rehomed. It’s a sad reality of pet ownership, and it doesn’t inherently make somebody a bad person, as long as they go through the proper rehoming channels. There’s a significant difference between leaving a cat in a cage in front of a storefront, letting it out into the street like Audrey Hepburn in Breakfast at Tiffany’s, and surrendering it to a reputable shelter in your area. The latter is the ethical option.
When you give your pet up for adoption, that’s it. There’s no going back after that. The damage to the relationship has already been done, and the new owners have no reason to give the pet back just because the previous owner regrets their decision. It’s the right decision to give up a pet if you can’t take care of them anymore, but that doesn’t mean you can get them back once you get your life together.