Pigeons are nimble and hard to hit.
Those pigeons [a/k/a squab] have a much greater chance of escaping to freedom than the chicken you eat ever did, and experienced far less fear upon being killed than a chicken tripped up with a catch stick or netted and then stuffed into a killing cone to have its throat slit.[ Assuming your chicken ever was in a pen large enough to require a catch stick and wasn’t raised in a cage with no room to move around its short life.]
Wing shooting’s just a different way of putting meat on the table that serves the purpose of improving shooting skills. It’s less efficient in that the mortality is going to be lower than the usual poultry killing methods because some birds will escape, but more humane than the meat processor, and at least if you are shooting it yourself, you’re not doing like everyone else does - relying on someone else to kill your food for you to keep that uncomfortable part of existance out of sight and out of mind.
Killing for fun and killing for food aren’t the same thing.
If I had to kill all my own food, I doubt I’d become a vegetarian. Killing for grins is a little different, though.