A lot of people who say ‘check your privilege’ use it as a conversation ender. They mean ‘Agree with me or shut up’.
Check your privilege should mean ‘I think you should examine how not dealing with this form of oppression has shaped your opinions. Your opinions may change as a result or they may not. You can examine your privilege and still conclude that I am wrong.’
If you mean ‘Agree with me or shut up’, don’t hide behind ‘check your privilege’. If that’s what you mean, just end the conversation.
