Vegetarians supplement their diet with rice, corn, beans, pasta, breads and other assorted high carbohydrate ladened foods. Most veggies will eat some animal products such as dairy products and eggs, the true vegans will not eat anything coming from animal period (some won't even wear animal by products such as leather). Doesn't matter if it harms the animal or not, they flat stay away from any animal product.

It's not so much the animal activist, but they have other reasons as well. For some it is simply religious beliefs.