Yesterday I gave a quote from St. Pius X about Holy Communion. Today I delve, briefly, into the fact that the SSPX is not in full communion. Recently, the SSPX (the fraternal Society of St. Pius X) issued a statement explaining why they were right (and, apparently) why the Pope is wrong. Most of what was said, I completely agree with (hold on before you presume I am attacking the Pope). In short, they said "we believe this, so we cannot agree with you". There was a bit of presumption that Rome disagrees with some of the positions they were taking (though it appears they are likely correct).
Yet, even if they are correct that Rome disagrees, the issue is not something that seems irreconcilable. Many other people hold the same position that they do, and are in complete and proper communion with the Church and have nothing to repent of in their beliefs. So what is the big deal? There is a Catholic way to express disagreement, and a Catholic way to deal with that disagreement. There is also a protestant way to express disagreement, and a protestant way to deal with that disagreement (just look how protestantism was invented in the 16th century).
Sadly, all that we can see from the SSPX is a good and proper traditional understanding of certain issues of the faith, and a seriously problematic manner of handling that understanding. It is not my place to tell them whether their criticism is correct or not. It is also not the place of the SSPX to tell Rome whether its criticism is correct or not. There is a certain humility and acceptance of persecution (albeit, some pretty harsh persecution) from authorities that is not being seen by those in the SSPX. A person can be right, but not have the authority to rule on that "rightness".
To tell the Holy Father that he must accept your position (even if you are right) is not generally how Catholics do things. Protestantism was created by people who wanted to be their own Pope. I do not believe that is what the SSPX is wanting, but it is hard not to see it in their actions. I pray that they can resolve this, but it will take humility and wisdom, and that is not standing out very much right now. Even if they are correct in their theological concerns, there is also a correct moral way to move forward. Let us pray that they all find it; very soon.