[Pink Pegasus]

Didn't something like this happen before with a housemate that wanted to leave in the middle of the night, and doesn't Big Brother say something like:
"We cannot let you leave right now, because Big Brother needs to have a few hours to make the "necessary arrangements" for your leaving"-or something along those lines. This could give them time to change their minds.

I don't think either of them actually want to leave, but that they are both trying to impress each other, so neither of them wants to lose face in front of the other, by being the one who backs down and changes their mind after all their talk of leaving.--because of this I wouldn't be surprised if they did leave to save face, unless they somehow mutually change their minds and agree to stay, or if BB convinces them to stay.

-but yeah, I don't think they really want to leave, but they might be afraid of looking stupid if they stayed now after all their talk.