Processing my own chickens has certainly been a profound learning experience for me. Like so many of us, I've had a sheltered lifestyle that didn't include these messy details concerning where my meat came from. In times past and today in many other places in the world, this discussion would never take place. It is simply a part of life, which involves sacrifices on others' behalf. This awarness can serve to make us more grateful for, and appreciative towards the sacrifices made by others for our benefit.
Just like you gain more appreciation & gratitude for your parents after you have your own children, only then fully realizing the extent of their sacrifice for you.
It's difficult for many of us to have to kill something we're not angry with, or afraid of, or disgusted by. To calmly take a living creature, especially one well known, and end its life in order to eat it. And it's still not my favorite part of the whole deal. But I look at butchering as I do harvesting my garden produce, and it would be as wasteful to let fruit grow, ripen, and wither on the vine as it would to keep some chickens alive until they died on their own. On a practical level, it would never be feasible for every chicken to live out their lifespan as pets. It makes sense that some of them are intended to be food for us. And because I care for my chickens, even and especially the ones I've raised from chicks, the final kindness I can show them is to give them a humane, swift, efficient & effective ending.
And I too find that my home-grown chicken has a much different, more pleasant feel to it than the icky slimy store-bought stuff. And I also hate to waste even a morsel of it, knowing how precious its source. I usually make it stretch by cooking it into soups, stews, chilis & salads. And I'll scrape the pot clean with a spatula, not wanting to leave even a shred of meat behind.