I think you missed the GP's point. Plenty of atheists/agnostics are vegetarians/vegans. You don't have to believe in God or the supernatural to believe that unnecessary suffering, to humans or animals, is wrong.
"But animals eat other animals, so it's natural!"
If eating meat is natural because animals do it (and if something that's "natural" is also "good"), then rape, incest, and shitting in the same river that you drink from would be just as tolerable. However, our highly evolved brains allow us to circumvent Nature's cruel impulses with reason and empathy. We can use science to figure out that shitting in the river is a great way to spread disease, and we can use empathy to understand that raping your co-worker after the Christmas party wouldn't be quite as fun for the co-worker as it would be for you.
Nature, "red in tooth and claw", is both cruel and amoral. However, there is no reason why we have to be like Nature.
To paraphrase Richard Dawkins: our genes gave us our brains, but our brains have the power to subvert the will of our genes.
"Why care about chickens and pigs when we don't give a shit about mosquitos, fungi, and cancer cells?"
While I adore George Carlin, I think he's slightly off the mark here. We care about chickens, pigs, cows, dolphins, etc. because they are mammals and birds. They possess complex nervous systems that can sense pain, adapt to their surroundings, and protect their kin. Most can learn, socialize, and even dream. In other words, they're a lot like us.
If I cut the limb off a tree, I know it won't scream. It doesn't feel pain, because it's not equipped with an apparatus to sense pain. Why should it? Pain is a response to external threats, designed by evolution to rescue a creature from something that could destroy it. Pain teaches me not to touch the hot stove again, and the simple idea of pain is powerful enough to make me flee from hungry wolves, even if they haven't nipped me yet. A tree has already prepared its defenses: a thick coat of armor against predators, and waxy, water-resistant leaves for storms. If a tree is in danger, it can't fight or run away. It just sits there. A tree that could sense pain would be the product of cruel and wasteful design, indeed.
Do mosquitos and flesh-eating bacteria sense pain? I don't know, but I'd guess they experience some limited form. Even so, I do know that, as parasites, they are quite a nuisance. The amount of suffering/pain/disease they inflict on more complex life forms far outweighs the amount of suffering I might inflict by killing them.
Keep in mind, death != suffering. The Humane Society puts stray dogs and cats to sleep because letting them run free or starve is more hazardous and painful than allowing them a peaceful release.
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Anyway, I'm starting to ramble, so I'll be quick with my final point: the GP asked to limit your meat consumption gradually because it is impractical and uneconomical for society to stop all at once. Buy meat from animals that have had their suffering reduced to minimal levels. Only you can create the demand for such products, because you have the choice. Eventually, forgoing all meat would make the vegetarian groups happy, but they are willing to compromise with reduced levels.
One day the technology may exist for us to "grow" our own meat without a brain or nervous system that has to sense pain and suffer. We might design our meat without gristle and bone, concentrating on the most tender and delicious cuts. It might even be cheaper than growing real meat the old-fashioned way. At that point, many will finally consider it unequivocally immoral to kill animals for food (barring famine). Much like how we see slavery today, they will look back at our ancestors and ask how an entire civilization could exist that engaged in the wholesale slaughter of innocent life, pumped through factory farms and made to sleep in its own filth at night.
Because meat tasted good? What the fuck?
