Skyrim Logic

I've actually yet to kill a chicken in Skyrim. My grandparents had them when I was a kid, and I literally grew up (to the extent of their lifespan) with a couple of them. I would go there every day for hours (up until like the 1st grade or whenever full days of school started) and carry around my favorite chicken. I had this one that was the runt of the flock; four year old me named it "the little chicken." I was super creative and original back then, but it really was tiny compared to the others, even when it was full-grown. Anyways, this thing was tamer than my golden retriever. Eventually my visiting cousins or something brought a dog to my grandparents and it attacked the chicken coop, killing the little chicken (and no others, even though there was like 20...) in the process.

tl;dr, there's no reason to kill helpless Skyrim chickens because you just know that there's some young Skyrim boy that has trained it and become overly attached.