This is a question which I am asked too often as most of my friends aren't vegetarians. There are certain reasons which I haven't been able to explain to them. Before I write this, I would want to say that I have no issues with people who are non-vegetarians. It's my personal belief and whatever I am writing, I confine this philosophy to myself and would never impose it to anyone. I would feel good if anyone understands and appreciates the reasons for adopting vegetarianism. But if someone has contradictions to my statements below, it's human right to have one's own beliefs and philosophy and anybody in this world is free to have those contradictions.
When I think about it - the first reason that come to my mind is why should I consume the flesh of other creatures who are being ruthlessly killed just for some short minutes of pleasure to my taste buds. Thousands of innocent dolphins die every year while fishermen are in urge to catch Tuna, the most sold fish. I am thankful that I am born as a human and I am not scared that anytime, anyone could just stab me for their taste buds.
Also, I feel God did not give humans the nails and teeth like other meat eating animals. So genetically, we have not been engineered for consuming flesh. Also the animal flesh has very high content of uric acid which is the cause of many diseases in human body. Also a non-vegetarian person carries much more content of toxins and disease organisms which are transferred from animal flesh which doesn't go even after being cooked. Human intestines are long, not scientifically engineered to digest such high amount of toxins. And one important reason I may not want to forget, animals are not sanitary conscious like most of the humans. And ofcourse i would not want to elaborate more on this.
People go to temples to search God. However the true temple is within, and the search too starts from, and ends within. I had experienced the killing of a dog(in a car accident) near a temple. After that, I witnessed a "puja" of that place by the caretakers of the temple because as per them, the place got polluted by shedding of blood of an innocent and to empathize the poor fate of the innocent soul. And if you cannot have a killing in a sacred place like temple then how can one create a temple inside oneself when there is flesh of some innocent being consumed every other day. This is the reason why mystics advise people to follow vegetarianism.
The law of Karma also explains this well like Newton's first law of Force that every action has an equal and opposite reaction. We carry the burden of our bad "Karmas" along with us which we have to shed here itself in one form or other, in form of one pain or other. Then why we humans, for our our taste buds which does not last longer than few seconds, just overweighing those burdens.
Consuming protein rich vegetarian diet is much more economical, social, ecological, humane and spiritual. Then why to complicate life of ours and others who aren't as fortunate as us, being born as humans.