Politics in the Catholic Church is seriously byzantine (see Wikipedia's Hierarchy of the Catholic Church)...
The title 'Pope' is an honorific. Technically the Pope is the Bishop of Rome and the Patriarch of the Latin Church, meaning that he acts as the titular head of the Church as a whole, mainly through pride-of-place as the bishop of the central diocese of the Church. Most of the heavy work of running the Church and setting pastoral agendas is handled at the diocese (district) level by bishops. There are also patriarchs and archbishops who are (respectively) titular heads of multiple dioceses or bishops of metropolitan dioceses with extremely large populations, but that is more of a status title than an added source of power. Cardinals are bishops who have been tapped as the Pope's cabinet or privy council; they have tremendous status and influence, but not greater authority in the direct sense. Bishops sometimes form Episcopal Conferences — semi-permanent institutional bodies — where they can discuss regional issues and problems with the Catholic ministry in specific areas. And to top things off, many Bishops also belong to a Catholic order (Jesuit, Benedictine, Carmelite, Franciscan, etc), where each order has its own distinct interpretation and practice of the faith.
In other words, it's a mess. The Church is hierarchical on paper, but in practice it is a kind of spiritual oligarchy, where a caste of people putatively rich in religious idealism compete for different visions of the Holy Church. The Pope is in the unenviable position of pressuring and cajoling a bunch of strong-willed, independent idealists into something like a coherent and consistent whole, all the while presenting a face of placid unity to the outside world. It is the quintessential 'herding cats' situation; one expects a lot of yowling and scratching.
Bishops are expected to conform to the Pope's decisions, sure. But they are given a decent amount of latitude to run their diocese as they see fit, and the only real weapons the Pope has to get them to toe the line are drastic: removal from office or excommunication. There is a notable risk that drastic actions from the Holy See might produce schisms in the Church and unrest among Catholic parishioners, who often think very highly of their bishops. No church leader wants the appearance of internal strife, so all of them have the incentive to haggle and negotiate for the benefit of the faith, but it is not at all uncommon for a bishop to make a bit of a stink when he feels the Bishop of Rome is leaning in the wrong direction.