#1 The Young Bucks turn heel and cheat to win
During the whole process of Hangman's change in character, he hasn't really acted like a true heel. He's just come to do business in the ring and then leaves when it is finished. Page has tried to get a word in when both teams have been interviewed. During the questioning, the Bucks are treated like the more important subject or the interviewer doesn't give Page time to answer.
For that reason alone, it's easy to see why he'd be a bit frustrated. He still chills with the fans after matches so that isn't a heel move either. The Bucks, on the other hand, acted like heels during their interview on Dynamite, claiming that Page was "nothing but a jobber" before they took him into the Bullet Club. They still consider themselves the best tag team in the world even if they aren't holding the titles.
The whole situation has been presented for Page to turn heel and completely sever ties with the Elite. He hasn't been bad to Omega, though, so it could easily be a misdirect in order to have someone else turn heel. Both Omega and the Bucks claimed that they thought they'd already be atop AEW but things have played out differently. They could easily turn on Page and/or Omega and cheat to win the titles they thought they should have already won. It would set things up nicely for the next few months as the Elite would fracture.