This is the point that continues to bother me. With this logic, and no additional context, I have a hard time buying the argument.

UA changes seats on people all the time, men and women. That's not considered a denial of service, so I don't think that's the right way to look at it.

What I've gathered from the discussion in this thread is that the motivation makes a big difference. If you force someone to do something and the intent is motivated by gender, religion, etc., it's discrimination. But no one knows that unless you tell them that, or otherwise document it. If the GA had never explained the reason for the move, the woman would have still been upset, but not claiming discrimination.

But moving someone from a seat for all kinds of other reasons is not a denial of service. Kicking someone off the plane or not providing them the class of service they paid for would fall under this category, but that didn't happen here.

If the GA hadn't given a reason, this thread wouldn't exist.