I am thinking about starting a vegan diet.
Have fun with that. Veganism is totally abstaining from any animal products. 
I've done the vegetarian thing before, but never full vegan. I'm doing it for health reasons. Are there other reasons to become vegan?
None that I can think of. You basically can't even eat eggs or drink milk. 
Yeah, it'll be a big change. But the benefits will outweigh the negatives, hopefully.
Supposedly it helps reduce the risk of heart disease if you plan well. 
Are there people that shouldn't eat a vegan diet?
Yeah, children or teenagers are not recommended to eat a vegan diet.  Also pregnant women. 
I can understand children, but pregnant women surprises me.
Well I guess it depends on who you talk to. American authorities on diet say it is ok.  The German experts say it is not ok.