With all the controversy that surrounded the election of Pope Francis upon the resignation of Pope Benedict in 2013, it seems that Catholics may have lost sight of a very key element of this episode, namely, that Benedict XVI never resigned his papal office, but only the active exercise thereof.
On the eve of his resignation, he said: "Anyone who accepts the Petrine ministry no longer has any privacy. He belongs always and completely to everyone, to the whole Church... "The 'always' is also a "forever"-- there can no longer be a return to the private sphere. My decision to resign the active exercise of the ministry does not revoke this." (General Audience, February 27, 2013)
According to these words, Benedict XVI remains pope, with no revocation of his office having occurred. According to Church law, a pope must give up "his office" for his resignation to be valid. (Canon 332) Pope Benedict clearly chose to retain his office "forever," which means he is still pope, which means that Francis cannot be pope, since there cannot be two popes. The late Fatima expert Fr. Nicholas Gruner points this out in a rare video on Benedict XVI's resignation. If Francis is the pope, then Benedict's office is revoked, but Benedict insists it was not revoked.