I have read/heard at many places where Goodbye is not good. It is a final remark on that very harsh moment.
Scene #1: Mike and Sarah are in good relationship.
"Hey honey, see you tomorrow. Bye!"
Scene #2: Mike and Sarah are now about to break up.
"I don't want to see you anymore. Goodbye!"
You get an idea? The given example is in the context of a relationship but it can be anything. Say friends getting angry at each other and decide not to talk forever. Earlier, they used bye and now, there is final goodbye.
In simple words, is goodbye a final bye?