[git] Why do I have to "git push --set-upstream origin <branch>"?

My understanding is that "-u" or "--set-upstream" allows you to specify the upstream (remote) repository for the branch you're on, so that next time you run "git push", you don't even have to specify the remote repository.

Push and set upstream (remote) repository as origin:

$ git push -u origin

Next time you push, you don't have to specify the remote repository:

$ git push