Liberal Cardinal Bergoglio tries to convince Pope Benedict XVI to accept his resignation, unaware the conservative pontiff is sizing up his harshest critic to lead the Catholic Church after his shock departure.

It was important to me to get across they had opposing ideologies. I take on board your comment though. Perhaps just "Liberal" would suffice. The frustration he feels is probably obvious by his desire to resign and the fact he is Pope Benedict's harshest critic.

I feel like this needs rewording. It's hard to get past the 'Frustrated and liberal' part. It is important to say both of things together like that? Maybe just put 'frustrated'.