@ Dobielover - It is hard not to be attached, but here are some things that have helped me.
I tend to keep a flock, where birds come in and go. I give them a good life while the are with me. As Bobbie says "Just one bad moment." I do allow myself to have a few favorites, but others I am more distant with. I think the longer you have chickens, you come to realize that loosing them is more of a fact of life with a much less life span that many other pets.
I do see posts where people are crushed by a loss, and sometimes question if chickens are a good hobby for such sensitive people. A lot of chickens will die of natural causes somewhere around 3 years of age. I know some people have birds much older, but I don't think it is a reasonable expected outcome.
Once I decide a bird has to go, I don't watch them. Just feed and water them. Distancing myself. The first one is the hardest, it does help to have moral reinforcements, but after a while, it is like pulling a sliver out, it hurts to do it, but almost immediately the flock is better.
Mrs K