Why is it wrong to eat dairy and eggs?
For a cow to give milk, she must first give birth. Therefore, the cows are impregnated, and the calves are taken away from their mothers immediately after birth, so that all the milk will be consumed by humans. The male calves are either slaughtered immediately, or raised as veal. When the milk production declines, the cow is reimpregnated, and the process repeats itself. When the cow is around six years old, her milk production permanently declines, and she is sent to the slaughterhouse, even though the normal lifespan for cows is much longer.
With regards to eggs, most male chicks are killed at birth, both for caged and for cage-free eggs. Also, even the cage-free operations still crowd the hens together, cut off a portion of the birds beaks, and kill the hens when their egg production declines. Egg laying hens are by far the worst treated of all farm animals, far more so than the animals raised for meat.
Follow up question:
Why don't you focus on passing laws requiring better treatment for farm animals?