It's important to be very clear: you're misrepresenting the options!
It's not a choice between suburbia and Manhattan. It's a choice between exclusionary, backwards suburban zoning (which is subsidized by denser development due to the increased cost of utilities for sprawling development), and literally any more sane option. Let people build duplexes, corner stores, local markets, and get rid of the cul de sacs. That's literally the core of the "density" people are talking about. Not Manhattan style high rises.
Saying that people (really any group, but millenials here) prefer suburbia because that's what you see them currently buying on the housing market, is ignoring the fact that the available housing stock probably doesn't match up to their preferences! Plenty of people are buying the "lesser of two evils" rather than their dream home. Plenty of people would choose something within walking distance of a decent park and grocery, if they had that option. But America, despite being built on the train and the pedestrian, has been rebuilt on the automobile and the cul-de-sac with single family home zoning. So people are buying what is available, even if it's not what they want.
If you doubt what I'm saying, check the prices of homes in prewar "streetcar suburbs" which are denser, but still have small yards, detached houses, and yet are near small commercial uses too. Plenty of people want to buy these and the prices have skyrocketed: it's illegal to build them now, so the supply is limited.