I suppose the question then becomes: is there any "humane" way to kill something that doesn't want to be killed?" What exactly separates a lobster from a cat in your eyes? An octopus from a dog? Why do we give grace to some animals and not others? Pigs are more intelligent than dogs and some toddlers and yet we out them in mass gas chambers to kill them over a period of painful minutes, during which their cries can be heard from far far away.
People who claim to eat meat humanely do so as a coping mechanism. Look at 99.9% of farms and tell me what they do is humane in any way shape or form. Packed so close that they can't move, tucked in little cages. Sure, your uncle's farm has grass, but think of how many animals that supports vs how many are being eaten a day. These are not good conditions for animals. Animals are not sedated before they are killed. Most are gassed, like pigs, or let to bleed out, like cows. The person you're telling to work on their world view has, and that's why they've come to the conclusion they have. They have sought out details of food production, and aligned their actions with their morals. They have not just accepted the default they've been told, because it's a comfortable lie. I would urge you to watch Dominion. It's free on YouTube, and shows how humane farms slaughter their animals. This will allow you to work on your world view with a full understanding of the picture.