This is just my opinion, but comparing the home that I was raised in to those of my students that I've had in the past and have currently teaching high school, I can't help but think that how much parents reinforce (or do not reinforce) lessons learned at home is vastly underrated, or in some administrative circles, flat out ignored. My parents did support me financially for school, and impressed upon me how important it was to get good grades, go to college, and become a productive member of society, but that message was also being told at school. A specific example I can give is how I talk. I was born 50% deaf, but my parents didn't find out until after a hearing test was given when I was two years old. Immediately, I received my first pair of hearing aids, started working with a speech pathologist (which continued until I was in sixth grade), and my parents reinforced those lessons at home - even if it meant getting into an argument over how I said something versus how it was supposed be spoken. Nowadays, all speech pathologists are very surprised when they hear me speak and see that I've had hearing aids as long as I have worn them.
I'm not sure, one way or the other, if millenials are all that different than my generation (early to mid-1980s), or previous generations post-WWII. But, I do have to present my lessons and the value of those lessons differently. When I was growing up, we were still raised on the point doing something simply because it's always been done that way and I (authority) told you to do it. Now, you really have to be able to show the reasoning beyond simply authority. So, to a student who doesn't want to do his schoolwork, I show that he signed a behavior contract in my classroom, show that the work he turns in is being graded, and the work he is doing is directly applicable to the skills/characteristics that future employers are looking for. I have found that for most students, if I'm effective in doing that, then really don't have a problem doing what I ask them to do. They do question a lot, but the onus is on us to effectively communicate what we're doing and why we're doing it.
One thing that I do believe has failed the millenials, particularly those that come from well-to-do communities as well as those that live in poverty, is the lack of enforcement on improper behavior or actions. There's a large number of young people who haven't experienced failure or consequences, and thus, given the opportunity to respond to that failure/consequence, or at least how to deal with adversity in a positive, constructive way. I'm extremely thankful for all of the financial support my parents gave me through the end of graduate school, but that also meant by age 25 or 26, I didn't necessarily know how to keep a monthly budget, how to prioritize money, how to save money, etc. I did have a false idea that since life was relatively easy financially when I was growing up, that's how life would be when I got married. Now, I'm a firm believer that adversity isn't necessarily a bad thing for the all of us to go through, but a lot of my students can't even deal with Google not giving them the exact search result in the 3-5 results, let alone what to do when they have a bad grade or lose job. That's scary, and I'm not sure that as a teacher, I'll be able to fully help them learn that without help at home.