I am thinking about starting a vegetarian diet. This means I would not consume the flesh of any animal.
That sounds healthy!  What are the advantages of a vegetarian diet over eating animal protein?
I'm not sure of the specifics, but health is only one reason for adopting a vegetarian lifestyle. Other motivations are political, cultural, or economic. 
What would be an example of some of these reason?  Is it cheaper to eat a vegetarian diet?
Yes and no. While many people save money from not buying meat, supplementing the vitamins and protein meat gives you can be expensive.
That is true.  Supplements are crazy expensive.  What political reasons are the for this kind of diet?  Is it because people don't want to harm animals?
People argue that animals have the same rights as humans. There is an activist movement, eco feminism, that believes oppression of animals and women are linked. 
Really?  I had never heard that before!  Do you know the reasoning for their thinking that it is linked?  Seems like a stretch to me.
The philosophy is that oppression of animals is similar to the privileged dominating others.