How can we morally justify taking someone else's life because we like the way they taste? We cannot justify harming others based on sensory pleasure. Harming someone else for one's own pleasure is morally reprehensible, and any good person knows that.
The words 'humane' and 'slaughter' put together, are what is known in the English language as an oxymoron, i.e. 2 words that contradict each other when put together. To use the term 'humane slaughter' is as nonsensical as to say 'humane rape', 'humane slavery', or 'humane holocaust'—regarding the latter point, some synonyms for 'slaughter' in the dictionary are 'bloodbath', 'massacre', and 'holocaust'... given that it does not make sense to use the term humane for any of those 3 words, neither can it make sense to say it for the word those synonyms derive from. Ask yourself this question: is there a nice way to kill someone who doesn't want to die? Given that animals want to live, and value their lives as we value ours, there is no nice way to kill them. In any case, anyone looking at the methods we use to kill farmed animals can see for themselves that it's not 'humane'. Whether the animal is stunned with a bolt gun or prongs, or whether it's by gas chamber, or whether they are killed via the Halal/Schechita method, these are not exactly methods we would use to euthanise even someone who did want to die. Regardless of the fashion of execution, there isn't a justification for taking the life. It is still taking the life of a sentient being, for your enjoyment ultimately. If somebody killed your companion animal, I doubt you'd say "that's fine because you did it humanely" as described above. Breeding innocent, defenseless beings for the sole purpose of killing them is not "treating animals well". If you want to treat animals well, you should support freeing them from being treated as commodities.
We already know that meat and animal products can cause the most common lifestyle diseases like heart disease, kidney disease and cancer, and that red and processed meat are class 1 carcinogens in the same category as cigarettes and abestos (meaning it's always unhealthy, wether you consume large or small quantities, just like smoking is). But you state that vegetables can also cause problems. I am very curious to know what problems exactly eating vegetables can cause, if you're eating a well-balanced wholefood plantbased diet? Because as far as I'm aware, it can reverse the aforementioned diseases?