"Imagine that you're sitting down to dinner with your family, and while everyone else gets a serving of the meal, you don't get any. So you say 'I should get my fair share.' And as a direct response to this, your dad corrects you, saying, 'everyone should get their fair share.' Now, that's a wonderful sentiment -- indeed, everyone should, and that was kinda your point in the first place: that you should be a part of everyone, and you should get your fair share also. However, dad's smart-ass comment just dismissed you and didn't solve the problem that you still haven't gotten any!
The problem is that the statement 'I should get my fair share' had an implicit 'too' at the end: 'I should get my fair share, too, just like everyone else.' But your dad's response treated your statement as though you meant 'only I should get my fair share', which clearly was not your intention. As a result, his statement that 'everyone should get their fair share,' while true, only served to ignore the problem you were trying to point out.