In response to sionnach's question about how animal products that don't kill animals are harmful:
One of the major reasons people go vegetarian/vegan is because of the treatment of animals by the food processing industry. For example, I don't think eating meat is morally wrong, however I do think the mistreatment of animals bred for consumption is wrong (plus I don't feel right eating meat, but that's just my personal feeling).
Animals used for milk, eggs, etc. are mistreated in the same way beef cattle, pigs, etc. are mistreated. People go vegan in protest against that.