What being a vegan is about is up to each individual themselves. There is no kind of contract which allows you to call yourself or see yourself as a vegan, and its furthermore very tiring when someone's trying to preach to you what veganism is about <fill in strict ruleset here>.
There are three global reasons one can decide to be vegan, vegetarian, and reducetarian.
1) Animal well-being.
2) Environmental well-being.
3) Personal health well-being.
You may substitute well-being with suffering, and there's also a nuance between death and staying alive but using (e.g. milking).
[EDIT: I suppose there's a fourth, a psychological reason how some people find certain products 'impure' to eat. But I'm not sure how I'd define that group.]