"The traditions of the church are not the reasons why they are excommunicated."
Actually, it's my understanding that they are.
The reasoning goes like this, I think:
(1) Modernists in the Church trying to destroy it.
(2) Nobody holding out except SSPX.
(3) Can't do that without priests. Can't ordain priests without bishops.
(4) Modernists insist they will pick bishops, which means death of SSPX.
(5) To keep Tradition from being swept away and suppressed forever, it was necessary for SSPX to ordain bishops.
Yeah. The problem is that this is false reasoning. It is a Catholic dogma that the Apostolic See of Rome will always "hold out". Per the IVth Council of Constantinople:
The first condition of salvation is to maintain the rule of the true faith. And since that saying of our lord Jesus Christ, You are Peter, and upon this rock I will build my Church, cannot fail of its effect, the words spoken are confirmed by their consequences. For in the Apostolic See the Catholic religion has always been preserved unblemished, and sacred doctrine been held in honor. Since it is our earnest desire to be in no way separated from this faith and doctrine, we hope that we may deserve to remain in that one communion which the Apostolic See preaches, for in it is the whole and true strength of the christian religion.
I asked one of the SSPX apologists here about this and he told me that the Council was wrong, and said the same about Pope Sixtus IV's condemnation of "the Church of the City of Rome can err" as being "contrary to the holy Catholic faith" and as containing "manifest heresy" (Bull "Licet ea", Aug. 9, 1479). Go figure.