Back to add that I have recently rehomed a bird, and it ended up being an amazing experience. Coco was a parrotlet, sold to us as a male but I suspect he was actually a she, and we just weren't really jiving after six months together. Our lovebird, Lyric, was appearing to be a much better fit for our family and lifestyle so we opted to stick with lovebirds and look for a more suitable home for Coco.
I thought about it for ages, really, and finally gathered the courage to post a very honest and detailed account of her personality and behaviour on Kijiji. While I was willing to wait for the right home for her, within 24 hours the most wonderful person messaged me about her and we arranged to chat over the phone the next day. We had the loveliest talk, and it was abundantly clear he could offer her a superior home where she'd be his "one and only". When he realized I'd chosen him as her new home, he immediately made plans to pick her up (a 6 hour round trip!)... he was so excited to come and get her, I had no doubts about handing her over. I've since had photo and video updates - he is absolutely besotted with her and I couldn't be happier for them both! We agreed that if he ever changed his mind or could no longer care for her, I'd at least have first right of refusal to take her back again which has given me some peace of mind also.
I really think that rehoming needn't have all this negativity surrounding it, personally I've had a lot of guilt over it and society's view of rehoming animals and it needn't be the case. I've rehomed a horse in the past, who I no longer had as much time to spend with due to family considerations ... he went to a GREAT home at a beautiful facility that I can visit anytime I'd like (I mean, I cry in a most embarrassing fashion whenever I see him so it's definitely limited the number of times I've taken them up on that offer!). I've also rehomed a dog with anxiety (in the end, we were ALL truly miserable) .. that was a really tough one to be honest, but she was adopted by her foster family who were fully aware of her issues and she ended up having a much better quality of life with them, so that was a success too.
The one thing Coco's new owner appreciated the most was the time I put into summarizing who she was. He said her ad really stood out compared to all the other ads he'd been looking at that simply read, "Parrotlet" or "Cockatiel". Something I wrote about her resonated with him and he felt like it was clear she was coming from a loving home where she'd been well cared for. At the very least, he knew what he was getting into and that there weren't going to be any surprises.
As lovely as it would be for every pet and new owner to mesh perfectly and for there to be no behavioural issues or life changes, at all, ever, it's not realistic to expect that every pet will find their "forever home" the first time around. Let's be honest, not all birds have the personality to make them good companion animals, and may be better off as breeders left to their own devices or in a home where there are fewer expectations (e.g. handling) in place. I think we're too hard on ourselves when it comes to this "forever home" business, honestly. Most of us, as responsible and educated pet owners, are doing our best .. and that's all we can really do!