Why would Cantor remain mum? Maybe he knows and likes Petraeus. Maybe he thought it was classified info. Maybe he thought disclosure would hurt the GOP if the public associates Petraeus more closely with Bush than Obama. Maybe all of the above.
It was classified
Perhaps Cantor knew, and it was classified info, so, he wasn’t allowed by law to go public. It’s sounds like he told the FBI and they sat on it until after the election.
Didn’t know enough of the details. It could have been a honey trap. The FBI and others needed to find out if there was a security breach. It could also have been false.
As for the resignation there is another reason he had to resign is the affair started and went on when he was a commissioned officer not just head of CIA. That is a courtmartial offense (adultery) and in his career he would have overseen judicial and nip activities involving this.