I have sympathy for all the birds we kill, they are not exactly pets but they are not faceless chickens queueing up for slaughter. Most of them have names.
Once the neck has been pulled, chopped or slit (whatever way) they turn from being chickens I know into meat for the table and then they become just something to be processed.
I can understand that you think you should feel more sympathy for them but if you are like us, from the outset we always knew that each and every chicken will eventually meet the same fate and have been mentally & emotionally prepared before hand, then it takes away the 'I'm a soulless chicken killer' feeling and makes it a 'I'm doing what I planned, and I'm doing it well' feeling.
We caught a wild junglefowl two days ago that had been bothering our chickens and I killed it there and then and I felt worse about that than I do with my own because it wasn't part of the plan, but when I put it into a predatory context (i.e. it was harming / could've harmed our chickens) I felt fine. Last night we had it in a red curry and it was delicious, probably more tasty than ours !
Don't beat yourself up about not beating yourself up - To quote Shakespeare.... 'That way madness lies'