Good point. A paradox is something that produces an unexpected contradiction. It must be unexpected, otherwise any trivial false statement such as 2+2=5 would also be a paradox. Russell's paradox is a good example since no one expected a contradiction. The birthday paradox on the other hand does not produce any contradiction, so it's just a case of sloppy labeling.
> the birthday paradox is a paradox for anyone who doesn't already know it
It is a fate of any solved paradox. A paradox is a confusing paradox only to a point when you learn where the contradiction comes from, and how it does it, and how to avoid it.
