You can't distill that into something as niche as your example, especially because your example lacks the social bias of privilege that one group has over the other. You're stripping that aspect from the conversation with your example and thus making your example moot.
"Moot" isn't the word your looking for here; "inapplicable" or "not analogous" are better choices.
Still, @Arkandel has a point, and it is this: it is difficult to motivate someone to engage in a serious conversation or discussion by using pejoratives or put-downs.
I think we have thoroughly discussed why "Not All Men" and "All Lives Matter" are offensive to marginalized groups.
So, back to trying to come up with solutions: how do we try and address what appears to be an ingrained mentality in our community?
There are times when it makes more sense to back away from a conversation with one person to have a more productive one with another.
It seemed clear to me that you and @Lithium were missing one another in the night.