Hey, I'm a vegan. I don't eat animal products and also have an associated philosophy against using animals as a commodity.  
Is a vegan diet more healthy than a diet that consists of animal byproducts?
Sometimes... It depends how careful the person is balancing their diet. A well planned vegan diet reduces the risk of some chronic diseases, like heart disease. 
Really!  I did not know that!  Isn't it expensive to eat a vegan diet? 
I don't think so. If you're careful about cooking full meals and buying bulk packages of beans and stuff it's not too bad. Weather the person does it for health reasons or ethical reason, it's still known as a vegan.
Interesting.  As a vegan, are you able to eat butter or drink milk?
No, vegans don't consume any animal meat or products like eggs, milk or ever honey. 
Even honey?  Honey is not a part of an animal though.  Do you miss eating desserts and stuff though?