The truth is they cannot afford homes in the cities they'd prefer to live in. This is supply & demand, and local city councils are artificially restricting the supply while demand is high, which only increases supply, and interest rates are at their lowest, which also increases demand. It's a simple econ math model.
Millennials need to move to suburbs and other towns which have more affordable living. Just because they want to live in city X doesn't mean they deserve it.