There is no good reason to. Being able to eat meat is not a good reason to do so. Out bodies do not require it, they simply have the ability to digest it. That is why all humans, regardless of diet, are omnivores - we are all able to digest both plants and meat.
As to reasons why we implicitly should not eat meat - simply, the factory farming system we currently use to produce our meat causes very real pain and suffering to millions of animals, throughout their lives until their slaughter. These are lives that are created by human intervention via artificial insemination, whose well-being is not looked after beyond what is profitable, that suffer mutilation without anesthetic to reduce costs, and are led to slaughter for no other reason than to feed human appetites for meat.
The animal's suffering is not necessary, and therefore is barbaric. To fund this practice by purchasing meat in full knowledge of these practices is equally barbaric.
A vegan diet is perfectly healthy. People often think that a vegan diet mainly involves eating carrots and lettuce. Where's all the protein, where's all the calcium!?
The truth is that a diet of only carrots and lettuce would be as nutritionally beneficial as a diet of only big macs and fries. The point being: whatever your stance on the ethics of meat consumption, you diet must always be well-rounded and varied. If you do eat meat, this means getting some portions of veg on the side, or cooking your meat in a healthy way instead of deep frying everything. Likewise, if you're vegan, this means rotating your meals smartly, so as to ensure you're getting a mixture of fruits, vegetables, pulses, grains, pastas, and oils.
One of the few benefits of the vegan diet being such a niche in society, is that most easy (and usually unhealthy) food sources, such as takeaways, ready-meals, and pre-packed meats are off-limits, forcing you to cook your own food from scratch more often, and easily recognise what you're actually putting into your body.
A vegan is likely to already have the knowledge of nutrition and variety of recipes required to give their children all the nutrients they need. If you do this, there is nothing wrong with raising your children on a vegan diet at all.