As if the chicken had a chance when you kill it "with your hands"... No reason to be condescending towards another's hobby.
Besides, it's not about the chicken having more chances or less. It's that it's a more substantial lesson in "killing one's own food" -- as we eat chicken, beef etc tons of times a year, whereas hunting is 100% hobby and 0% substantial "killing own food".
So make that at worst 50-50. And there's a lot of poorer people out there for whom the annual deer is a significant and cheap source of high quality meat.
And that doesn't count veggies (we did garden) plus the cereals that probably accounted for probably over half the calories we consumed.