...you've never actually listened to "Bad Day," have you? Or paid attention to the lyrics, obviously. He's not singing about himself having a bad day, he's singing about someone else, a close friend maybe, having a bad day, and its not even a literal bad day. The song's more about trying to help this friend out of whatever depression he's in.
And anyways, by your logic, Dream Theater are a bunch of whiny white guys because of "A Nightmare to Remember," an event which, in its simplest form, is a pretty bad day.