I was born in a year that traditionally was generally not considered "millennial" by demographers, but since it also did not fit with the years they used for previous generations, modern definitions tend to include my birth year as "millennial". This irritates me, because myself and most of those that I know who are my age don't fit the usual descriptions of "millennials" and we don't like the association. Now, I happen to like millennials. My wife is solidly in the millennial years. I have many friends who were born in the millennial years. But I don't like having the label applied to myself and I don't fit the descriptions at all.
In the end it isn't a big deal. I have no plans to ever call myself a millennial. But it is worth cautioning against stereotyping individuals because of the year they were born, as I unfortunately see many people do.