The Mediterrean diet is largely vegetarian:
http://www.abc.net.au/news/health/2017-02-16/10-commandments...
75% of the world's population loses their ability to digest lactose after infancy:
http://www.pcrm.org/health/diets/vegdiets/what-is-lactose-in...
Milk is for babies. Cow's milk is for cow babies.
Quoting directly from the link I provided:
If you think the Mediterranean diet looks a little low on dairy foods, you're right. It's certainly lower in dairy than is currently advised in the National Dietary Guidelines
...But traditional Greek Mediterranean populations got calcium from other sources: sardines and other small fish which were eaten with their bones, and from leafy greens (which contain only a little calcium but the large volume of the greens eaten meant the amount added up).
http://www.dummies.com/food-drink/special-diets/annual-chees...
https://www.livestrong.com/article/402645-what-are-the-healt...
At least some Greeks appear to have a genetic mutation that shields them from the worst effects of cholesterol and saturated fat in cheese:
https://www.express.co.uk/life-style/health/809612/greeks-un...
Even the recent cheerleading studies for cheese caution that eating it in large quantities is dangerous:
https://www.forbes.com/sites/alicegwalton/2017/12/06/is-chee...
And health issues aside, dairy is cruel: https://www.theguardian.com/commentisfree/2017/mar/30/dairy-...