Unity and Fraternity among Priests as Brothers of one sacerdotal family among themselves and under their Bishop is so important, so much more than is sometimes recognized; the very credibility of the Church's Mission very often depends on it. There is only one Church, not several. The Priesthood must be one and inseparable; brother Priests united in Faith and Charity among themselves, and subject to and under the Apostolic Authority of their Bishop. So too the Bishops among themselves and under the Authority of the Roman Pontiff. That is how the Church was set up and has functioned for 2000 years, even in times of crisis. That is part of the reason the SSPX, which is rather strongly united among itself, with 650+ Priests, and 3 Bishops, also sees the necessity of having a relation to Rome, and not entirely cutting off that bond. By it, we remain united to the other Bishops of the Church, to the Successor of St. Peter, and finally to the Universal Church in every place.
St. Ignatius of Antioch, disciple of the Apostles, Father of the Church, said this, on the obligation of all, especially Priests, to follow the Bishop; "But avoid all divisions, as the beginning of evils. See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid."
http://www.newadvent.org/fathers/0109.htmArchbishop Lefebvre, 1983: "However, in our day and age, alas! trials are all too common. Obviously, we are living in an age of confusion within the Church and we have to get used to such trials. However, I hope that the situation will be straightened out and that maybe some of them will come back to join us once more, that some of them will do some thinking, and that God will give them light.
In any case, I thank all of you here for remaining faithful to us, and we will remain faithful to you. We will carry on with what you have always seen in the Society. I gave Confirmation today just as I have given it in Oyster Bay Cove, in Armada, and elsewhere, in all the centers. I have changed nothing. So, I trust you will remain faithful and that we will be able to continue working together for the greater good of the Church, because there is nothing more disastrous, even in the face of Rome, than these divisions, because these divisions weaken us and weaken our fight for Tradition. So, let us pray that everything will be sorted out.
Personally, I am not seeking to harm these priests may God be their judge! And I ask you not to get into polemics, but simply to follow us. You now have here a magnificent chapel. Come and attend Mass in this chapel with the priests of the Society, and, in the various centers, bring about a regrouping of the faithful staying with the Society, so that they keep their bond with Rome and with the Church. It is very important that there should always be the bond with Rome if we wish to remain Catholic; even if we do not agree with everything being done in Rome, I think the bond is absolutely indispensable."
https://www.sspxasia.com/Docuмents/Archbishop-Lefebvre/Conference_at_Long_Island.htm