It is nothing like saying murder is wrong but hiring a hit man is fine!
Have you eaten horse? Would you? Why or why not? People around the world eat horse every day.
Have you eaten dog? Would you? Why or why not? People around the world eat dog every day.
I have eaten horse, they sell it in the grocery stores in Switzerland and I must say it was phenomenal. I would eat it again in a heartbeat. Though, if I owned a horse I would probably not eat it. I would love for someone to eat it, but I probably wouldn't.
I believe that when people make a connection with an animal they, naturally, have reservations when it comes to consuming the animal with which they have had a relationship.
If the person said they could never kill any chicken (theirs or otherwise) but they eat chicken, now that is like saying murder is wrong but hiring a hit man is OK. And when your talking about chicken murder or chicken hit-man, neither one is wrong!
ETA: I have four backyard, city hens and I am planning on eating them. Though it does depend on how long they produce eggs and how long I live in city. If I can get out of town and into some property before these hens reach their end I will probably let them live out their lives wherever we move. Since at that point I will definitely have a tractor full of meat birds and a big coop of layers. I figure letting my city hens live out their days on a nice piece of land is the least I can do for cooping them up in a little backyard for years! Though if we are ready to get new layers before we move then our current flock will be processed and eaten by my family.