Frankly, some cannot. We all start from different places. I grew up on a farm where the chickens gave us eggs and meat. To me it is just the way I grew up. Others come from places more like you. Everyone has different experiences. Yours are more with chickens being pets, mine are more as livestock. That does not mean you can't get to a place where you can eat your chickens, many people do, but you have to make your own journey.How do others steal themselves against emotions to where they are not only able to cull them, but enjoy them?
I never enjoy the killing, hopefully you never will either. There is something final about taking that life. I see it as something I have to do if I am going to keep chickens. My goals are for meat and to play with genetics, which means I have to hatch chicks and butcher them. Otherwise I would not have them. They would never have lived because I would not have hatched them to start with if I wasn't going to eat them.
I try to raise mine giving them the best life I can until they have one bad moment. I try to make that bad moment as quick and sure as I can. That life will be better than any grocery store chicken you buy. Mine get to chase bugs, scratch, take dust baths, and be chickens. Also, I try to respect the animal by using it all. I get the standard cuts we are all used to. I save parts to make broth, both saving certain parts when I butcher and reusing the bones after I cook the meat for the table. I use most of the organs, either for broth or to feed my dogs. I personally really like fried chicken liver. You may find this disgusting, but when I butcher I use two buckets. One bucket if for the parts I'm going to bury, either in my garden or in my orchard to feed the plants when it breaks down. The other bucket is for the parts that I feed back to the rest of the flock. That includes bits of fat, lungs and gonads, I even cut the intestines into 2" lengths for the chickens to eat. The only thing that goes to the landfill is the bones after they have been used for broth.
I don't know if any of this helps you or makes it harder. Good luck!