Intentionality is not relevant with micro-agressions. Parse the nomenclature all you like, but people unintentionally cause harm all the time.
The issue is when as a society, those things are so commonplace that they repeat over and over in a constant loop.
For example, if someone accidentally bumps into you while passing you on the sidewalk, it's no big deal, they apologize and both people move on. Now imagine that everywhere you go, people keep bumping into you and apologizing all day long, multiple times a day.
You know no one means anything by it, but the aggregate of all that bumping is terribly frustrating and you can't even take it out on any individual person because you know they didn't mean it.
That's what many minorities deal with. And white people are completely clueless to what they are doing.
No one is talking about punishing the micro-agressors. Just educating them so we can minimize the distributed bullying campaign that we have been subjecting people to and give them some breathing room.