Where I live (very large US city) buying actually works out better than renting IF you can afford a substantial down payment, which I imagine most millennials can not. My wife and I ('88-'89 born millennials) were able to and are saving money every month on the bottom line while living in a condo larger and nicer than our previous apartment.

Given the generally anemic savings and salaries/wages of most millennials, I think being able to qualify for a good mortgage is a major hurdle.