Being a Vegan doesn't mean that you'll be healthier than a non vegan but vegans have less of a risk of developing some diseases and cancer because of not eating meat.
Eating some meat especially chicken has been linked to developing cancer is some people but eating chicken doesn't mean you'll actually get cancer and many people do eat chicken and other meats and never have cancer.
Being a Vegan you tend to eat more healthy vegetables than a non vegan so in a way being a vegan could be healthier but even non vegans can be healthy and live a long life as well.