It's not murder, I'm sorry you feel that way.

It's culling, euthanasia, dispatching, or processing... depending on the final outcome. Murder is something that humans do to another human. It's out of cold blood or anger. Not out of concern or caring.
It's also not giving up on them. It's making a difficult decision to do what the keeper thinks is right for them and their flock.
I kept the first deformed female bird I hatched after a power outage. The deformed male was got by a predator before his time to head to freezer camp. Never again.
There are lots of roosters without deformities looking for good homes too.
Bless your heart for you tender perspective!
Learning about life and death and how to accept them are key lessons on any farm. I'm thankful to have the skill to help out a hen should she ever face emergent need due to injury or illness. And so grateful to know where my food comes from and how it was treated every single day including that very last moment and even after wards.