There are essentially three reasons to go vegan, each sufficient on their own: Animals, Environment, and Human Health.
Animals: The vast majority of animals raised for food live miserable short lives filled with suffering. In fact, there is so much suffering in animal agribusiness that more animals literally suffer to death before slaughter than are killed for all other reasons (fur, experiments, shelters) combined. We can easily prevent this needless suffering by eating vegan meals instead of eating animals and their products. Details are here http://www.mercyforanimals.org/farm-to-fridge.aspx and here http://www.countinganimals.com/is-vegan-outreach-right-about-how-many-animals-suffer-to-death/
Environment: Modern animal “farming” is environmentally destructive and wasteful. It is a leading contributor to today’s most serious environmental problems. More info here: http://www.vegansoapbox.com/the-connection-between-the-environment-and-veganism/
Human Health: Vegetarians and vegans tend to have lower incidences of disease, specifically heart disease, cancer, and diabetes. But there’s more than just disease caused by excessively eating animals. The more important health hazard IMHO are the diseases spread by animals. An increase in the demand for products from livestock animals is likely to result in an increase in the spread of infectious diseases. That’s due to overuse of antimicrobial drugs in livestock, overcrowding of animals that hastens the spread and mutation of disease, and waste from CAFOs that contaminates water and soil. Some more info on that: http://mahider.ilri.org/bitstream/handle/10568/21161/ZooMap_July2012_final.pdf?sequence=4 and http://www.pewhealth.org/projects/pew-campaign-on-human-health-and-industrial-farming-85899367226
The first reason, the animals, is the most compelling to many people like myself. It’s also the easiest to understand. Young children comprehend that whereas the other reasons require a bit more education. Moreover, the environmental and health reasons are modern problems related to the current human and animal population sizes. The cruelty, however, seems to exist no matter what year it is. Todays “factory farms” are seemingly immeasurably cruel and are likely far more cruel than farming systems even just 60 years ago. However, no matter the farming method the result is always the same: slaughter. Personally, I cannot justify stealing animals’ lives when there’s simply no need to. So while it certainly can be “more complex than just saying ‘Oh we don’t want to kill chickens because they get hurt!'” it doesn’t have to be any more complex than that. Basic kindness is not complex.
Any of the reasons above is a good reason to go vegan!