There are many reasons why you'd want to become a vegetarian. The easiest reason is that you might simply not like meat. Some people do not enjoy having to often clean their teeth using floss or a toothpick after a meal. Or you might also not enjoy constantly chewing meat that can sometimes be hard and just enjoy soft vegetables instead.
Some people like the idea of becoming a vegetarian because it is by far the most environmentally friendly way for humans to eat. There is definitely a link between your diet, linked to the overall diet of human beings, and the well-being of the environment. It's probably hard to understand what is mean by this at first glance but consider the amount of nutrients it takes to grow 1 pound of beef. It takes about 25 gallons of water to grow 1 pound of wheat but it takes about 390 gallons of water to produce 1 pound of beef. This is because it takes many years usually for the animal to grow and it has to be fed a large amount of food throughout its life. The production of meat, eggs, and dairy products places a heavy demand on our land and water. In some cases it also contributes to pollution. It takes a far greater amount of land resources to raise animals than it is to raise a comparable amount of plants. Animals place a heavy burden on the land because they cause desertification by eroding topsoil and drying out supporting plant life over time. In Central America and South America a large number of acres of tropical rain forests are cleared to make way for cattle to be eventually fed to humans.
Furthermore, raising livestock uses an enormous amount of drinkable water because pesticides, herbicides, and fertilizers used to grow food for the animals to feed on eventually pollute the land at a much faster pace than if we simply ate the agricultural products directly.
While it's not the animals that might directly pollute the land, by raising meat to eventually be fed to humans, the animal was fed with an enormous amount of food compared to what you end up getting in pounds of meat.