I have become a vegan, but not completely.  I have a lot to learn
It dates back to its  roots in the civilizations of ancient India and ancient Greece.
Why did the people stop eating meat?
It  was closely connected with the idea of nonviolence toward animals (called "ahimsa" in India), and was promoted by religious groups and philosophers.
Did people continue to drink milk and eat cheese, which is non violent?
 in medieval Europe restricted or banned the consumption of meat for ascetic reasons, but none of them abstained from the consumption of fish; 
Why was fish not included?  They are also animals.
Because veganism restricted the consumption of meat ,fish served as a better alternative
In history, when did people begin to believe eating meat is not healthy?
banned the consumption of meat for ascetic reasons, but none of them abstained from the consumption of fish; these monks were not vegetarians, but some were pescetarians. Vegetarianism was to reemerge somewhat in Europe during the Renaissance and became a more widespread practice during the 19th and 20th centuries. The figures for the percentage of the Western world which is vegetarian varies between 0.5% and 4% per Mintel data in September 2006. 
Ancient.
Ancient Indian subcontinent.
Ancient Indian subcontinent Early Jainism and Buddhism.
Jain and Buddhist sources show
History of vegetarianism
The earliest records of vegetarianism as a concept and practice amongst a significant number of people are from ancient India and the ancient Greek civilizations in southern Italy and Greece. In both instances, the diet was closely connected with the idea of nonviolence toward animals (called "ahimsa" in India), and was promoted by religious groups and philosophers.
Following the Christianization of the Roman Empire in late antiquity (4th–6th centuries), vegetarianism nearly disappeared from Europe. Several orders of monks in medieval Europe restricted or