In cass it's not clear from other comments, if the site tells you either one's wrong but not both, you can then brute force and try out a bunch of usernames and passwords to effectively farm for both: those that say "wrong username" means that the password is valid, while those that say "wrong password" means you got the username that's in the system.
Once you've collected them, the rest is just trying out every password for every user.
So... while this seems weird for a person, it is very much intentional.
Edit after several comments: I don't know why it's hard for people to look at the OP, take it for what it is, and argue for the sake of the argument, rather than claiming that something's impossible because of common or correct technical practices.