Well, part of the problem is how the lowercase reference of "millennial" gets pejoratively used against ALL young people (not just members of GenY).
I encourage my fellow Millennials to be proud of our accomplishments and our positive attributes, and to reclaim ownership over the term. Unfortunately, there's this default assumption (seemingly made by many) that power *should* go to GenXers, then "skip over" Millennials, and then go straight into the hands of Centennials/Zoomers.
Somebody please explain to me how that's NOT ageist.
Cross-generational solidarity, as you've suggested, is what we need!