It'a myth. Vegan diets are no healthier than meat-based diets.
A healthy diet is based on appropriate caloric intake (vs output), balanced proportions of carbs-proteins-fats, adequate vitamins, trace elements and minerals. To the degree that it may be harder to achieve the above, a vegan diet may actually be less healthy.
There are valid reasons for going vegan: religious/spiritual, moral (you hate killing animals), taste preference ( you don't like the taste of meat), adverse reactions to animal-based products. But don't do it for health.