What is wrong with "Qui avez-vous perdu contre"?
It is a word for word translation that doesn't work in french. The correct word order is Duo's translation.
Why do we use qui here? I thought that que was for objects of sentences and that qui was for subjects.
I think that you may be confusing "qui" with "ce qui" and "ce que".
"Tu as raté contre qui": what is wrong with this?