I have consistently heard rumors that the Orthodox and the Roman Catholics will be reconciling at some point (at least to the point of Catholics being able to receive Orthodox sacraments). Sometimes the rumors are that it will happen during a reigning patriarch, but other voices among the Orthodox have suggested that such a gesture is an impossibility*. So, which is it? Is reconciliation possible (and close), or will things continue as they have for nearly a millennium?
As to the differences from a Catholic man's perspective:
The metaphysical dispute over the Filioque, wherein is asked "whence comes The Holy Spirit"? A Catholic person says, when reciting the Nicene Creed, that The Holy Spirit "proceeds from The Father and The Son". Unofficially, this wording brings to mind the theory of procession put forth by St. Augustine (namely that The Father's contemplation of Himself is ontologically creative, becoming The Son; and that The Love between The Father and The Son is similarly ontologically creative, becoming The Holy Spirit). The Orthodox Church would see this formulation as diminishing the fullness of Godhood of The Holy Spirit, feeling that it subordinates The Holy Spirit to The Son and The Father---that is making Him less than co-equal with Them. The Catholic Church would deny that this is the intent of the formulation as adopted by Her, although it allows the formulation of St. Augustine as a perfectly valid one. More fruitful discussions between the two Churches has centered on asking what Each means by "comes" in the question "whence comes The Holy Spirit?"
- Furthermore, the Orthodox Church is quite upset that the Catholic Church unilaterally decided to insert "and The Son" into the Nicene creed, when it was not there before. They believe that modifications to the ancient creeds can only be done through the participation in an Ecumenical Council. In fact, one of the Popes in the Middle Ages agreed with this complaint from the Orthodox Church, but was ineffective in changing the practice of the West.
On Church governance & the role of the Pope vs. Bishops. Both Churches could fully agree, in principle, that the Bishop of Rome is "first among equals" regarding his relationship to other Bishops. But whereas the Catholic Church emphasizes "first" and regards this designation to mean that the Pope has "ordinary and immediate" jurisdiction over every parish (bypassing the Bishops altogether, in principle), the Orthodox Church emphasizes "equals", and thereby would place supremacy over the faithful on their Bishop, regarding the designation "first among equals" as a matter of honour only. Thus, the Orthodox Church sees the Pope's claim to supreme governance as a power grab which diminishes the dignity and office of the Bishop. It doesn't help matters at all that, historically, the Orthodox Church has felt slighted, disrespected in their laws and traditions, and imposed upon by the Pope over the centuries. While the Catholic Church firmly defends the prerogatives of the Pope's power of governance, She denies that such exercise diminishes the dignity and office of the Bishop, and continues to uphold that the office of the Pope (when it comes to governance) is a necessity of the communion of Bishops, and that the Pope is only the "first among equals". The difference in governance which causes so much ecumenical trouble between these two Churches can be summarized as the difference between a monarchical republic versus a true confederacy.
"Cultural" differences. For these two Churches to be united, they must agree that they follow the same Faith of times immemorial. From the Catholic perspective, this is easy enough: except for questions of the filioque, they see themselves as following the same Faith (that is, the same teaching). On the other hand, the Orthodox Church places a great deal of more emphasis on liturgy as part of Faith than the Catholic Church does. To the Orthodox Church, if a liturgy is recent, it is inferior. To them, the best liturgies are the ones that go back to eons ago, and if possible, to the very beginning. They barely put up with liturgical translations. They see the Catholic Church as having succumbed to the times in adopting novel---and therefore not good---things in their liturgy (beginning with the filioque in the Middle Ages and continuing to the recent changes in their liturgies to make them "more modern"). If the Catholic Church is seen as parochial for trying to keep a semblance of homogeneous liturgical practice by other Christian groups, then they certainly have not taken a good look at the Orthodox Church. Thus, to achieve union between the Catholic and Orthodox Churches, these issues of "culture" wherein the Catholic Church is seen as "modernist" by the orthodox Church must also be resolved.
So, is it likely that these two Churches will reunite? It is the hope and prayer of every Catholic person that they will. It should be the hope and prayer of every Christian that 'all [Christians] may be one', such as The Father, The Son, and The Holy Spirit are. At the same time, both of these Churches do believe that a union without a consensus on the deep issues that divide them is artificial, and not a real union at all. Thus, they both believe that they need to work on these fundamental issues beforehand.
And herein lies one of the problems. For, while the Pope can speak for all Catholic Bishops, ratifying their declarations, there is no one in the Orthodox Church that can similarly speak for everyone. If, and when, reunification takes place, there will always be a substantial amount of Orthodox Bishops which will renounce the reunion as heretical and will refuse to reunite.
Another problem: there are some teachings that the Catholic Church deems as irrefutable, due to the dogma of infallibility. To go back on these teachings would amount to a declaration that the Catholic Church is not infallible, which I fear She cannot do. The best The Catholic Church can do is to recast (re-explain) those same infallible teachings on a new light, perhaps making it logically possible to come to a formulation of the teaching which is also acceptable to the Orthodox Church. Given that both Churches have very gifted and careful theologians who feel themselves in the right, it is very difficult to see how this might be possible.
THEREFORE, what are the chances that both Churches would unite? Very unlikely, if you ask me. History may force them to reunite (and force them to work out those differences), if a world-wide effective persecution of both Churches should occur, but other than that, all we can do is hope and pray.
The Catholic understanding is that the lack of reconciliation is due to a lack of love when Catholic and Orthodox share in full all doctrines that would make full communion appropriate.
The Orthodox position is that there is much more than the clause in the Creed and Catholics are saying, in effect, "Let us restore communion despite our unresolved differences."
It is my own experience that Catholics who seek reconciliation never seek to resolve the unreconciled differences or otherwise acknowledge what they have to repent of for any appropriate reconciliation to be possible. The Orthodox experience here is kind of like the Catholic experience when Anglicans or Baptists want to share the chalice without changing any of their doctrines.
(See my own Open Letter to Catholics on Orthodoxy and Ecumenism.)