I don't like to look at people as "vegans" or "meat-eaters". No. No, I much prefer to see all these such people as "pre-vegans" - simply people who have not yet recieved the information that they need to be inspired to go vegan.
Surely, for everybody this reason will be different.
Personally, it was the health aspects for me - with a little bit of ethics sprinkled generously on top.
For others, it may be humanitarian reasons - wishing to end the starvation caused in third world countries by the western world's excessive meat consumption.
Some may be concerned entirely with the dismal treatment of factory-farmed animals.
Yet others may be moved by evironmental reasons.
Luckily, there are so many fantastic benefits to just about everybody through a vegan diet, so unless somebody literally does not care about anything there must be some aspect of veganism that will appeal to each individual.
At any rate, never be discouraged or inclined to stop sharing your veganism with those around you. You never know what could be that one little fact or statistic or picture or explanation that will just click with somebody.