You shed light on why it's so important for Generations X/Y/Z to have such support and solidarity for one another, where we can celebrate our own generational virtues without bringing other generations down.
In fact -- and please know that I'm not accusing YOU of this, Minimalist, as it may have been unintentional on your part -- the usage of "GenZer" can be subconsciously ageist toward Millennials, in terms of (perhaps subconsciously) placing Gens X&Z on par with one another (via positive implicit value-judgment) while relegating Gen Y to a status where we're essentially considered the redheaded stepchildren of the generational spectrum.
In my article on generational differences from earlier this summer, I talk more about utilization of language and terminology, and how we can employ it, in various ways, to uplift rather than diminish: