I am vegan. I first stopped eating dairy because of health (I suspect allergy because ever since I was little when I eat dairy I have got scratchy throat and occassionally like when eating a lot like a big glass of milk or some ice cream breathing would get hard and hurting, and other stuff too). Also I was going to the doctor for chronic sinusitis that has been recurring for years and that cleared up, and then I gave up the rest of the animal products for ethical reasons.
I remember when I was about 5 my dad telling me about how some Jains will sweep the ground in front of them to avoid stepping on insects, and I remember insisting on us doing this, as I would get extremely upset when someone would try to kill an insect or other animal and I would try to get an alternative whenever I could.
I also wanted to become vegetarian as a child and did so for a little while, but unfortunately we lacked good information and thought that it would be expensive and require special products like Morningstar burgers to get adequate nutrition.
I think the main thing is that we are taught early on how to plan meals around animal sources, and so any change from that will feel difficult and uncomfortable. (Such as when I was in about third grade after a lesson on the food pyramid, there was a breakfast of pancakes, eggs, a fruit, and something meat-based. Sure you could have vegan pancakes, tofu scramble, fruit, and tofurky sausage if you want, though myself I might prefer a lentil veggie soup and soy yogurt with fresh fruit, or maybe the occasional pancake or tofu scramble, and of course cold cereal in non-dairy milk is awesomely convenient and nutritious).
But, when I was at college, all it took for me was to see that healthy, yummy vegan food could be available (in my case, fortunately, the cafeteria caters pretty well for vegans), and suddenly I put my ethics into practice. Yeah, cheese was the hardest to stop, but there are some good alternatives (particularly I think mozzarella slices, and cream cheese alternatives tend to be more convincing and tasty). I probably wouldn't dive right into a cheese alternative right after having dairy cheese; I would probably wait at least two weeks or a month for cheese. If you don't like soy milk, there's also rice milk or even almond milk depending on where you are.
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"There are things you need not know of, though you live and die in vain,
There are souls more sick of pleasure than you are sick of pain"
--G. K. Chesterton, The Aristocrat