- A thin person tells a fat person that she is equally oppressed because she's been made fun of for being thin.
- A man states that if women want "real equality" then they can't expect to take maternity leave or be given time at work to breastfeed.
- A white person claims they face just as much racism as people of color because they swear they've been called a "cracker" one time and real fairness would mean the elimination of all slurs.
And as for the example of with the man who is talking about "real equality" for women, the problem is that his version of "real equality" is again ignoring the world in which we operate. It takes a man's situation as default and denies the sexism that women face on a daily basis. As I've said before, I feel strongly that you can't achieve an actually equitable society through expecting women to behave and think like men in order to be seen as legitimate, to get ahead, and be successful. My brand of feminism has never been about this. Instead, it is about making systems (which have always favored men in the past) also work for women. If we take how men do things as the standard and expect women to conform to that, we're simply validating patriarchy.
It's so much more important in each context, that we examine the "-isms" at play--the existence of oppression and the history of discrimination. The real problem is that when people benefit from white, male, thin, able bodied, straight, cis, etc. privilege, they don't want to compromise that position. So they deny the situation and instead talk about this false notion of equality which ignores the real world we operate in.
To me, it is much more important to think critically about how privilege affects our world and how we can work toward the eradication of various oppressions than to try to figure out some arbitrary standard of "equality."