Bishop Schneider may not be wrong. I'm not a theologian, so am unqualified to answer.

The SSPX also mentions the pope in its mass; same as Lefebvre did. Thus, not intentional.

The SSPX are the ones walking away, this time. They were offered dialogue in oder to find a way of recognition and regularization. Bishop Athanasius Schneider has also said that they should take up the offer to dialogue in addition to Rome recognizing them, and working out the details later. It is a legitimate use of Papal authority to ask for a pause on consecrations, and seek clarification on a regularization in the Church, so, I can't support them in this. Its a tragic tale being played out with entrenched and hardened attitudes on both sides, and both sides have some degree of fault.

Ummm. No one is walking away. The SSPX went public because it was getting stonewalled by the Vatican. Also, the pope has not talked to the SSPX. The porno cardinal asked for a pause. My guess, Tuco made a ridiculous precondition (1) to confuse the discussion and (2) to have an excuse to continue stonewalling.

The CDF works under the directives and at the discretion of the Pope. No, matter how bad Tucho's theology is, they SSPX should have agreed to dialogue and discussion. So, yes they still walked away. They don't want to talk to Tucho, fine, but you dont just demand to see the Pope and expect him to jump. As a Catholic you don't get to tell him what to do. He's not at your discretion.

Tucho's precondition was designed to not talk! Pope Wormy II (from the apparition of La Salette) intends to stonewall SSPX. So long as Leo and Tucho stall, they prevent the expansion of the Latin Mass. They agreed to dialog, but they will not (In My Opinion) concede anything. They want the automatic excommunication of SSPX and the elimination of TLM.

From the Communist playbook: Eliminate the sexual taboos. This destabilizes the existing structures which makes it easier to install new structures. This explains the Vatican's huge emphasis on LGBT. These are machinations of man.

@philosopher No, they are not "walking away". It is quite evident that Rome has no intention of granting them Bishops. They were only granted "dialogue" on the condition that any question of consecrating Bishops be abandoned. Sorry, that is evil and anti-Catholic. Eve brought about the ruin of the entire human race because of invidious "dialogue" seeking to thwart the Will of God.
The SSPX has more than half-a-million souls in their care. A Bishop's duty is to ensure that the souls in his care are provided for. The SSPX knows that without Bishops, their chapels will be closed, their seminaries shuttered and their schools vacated. No Bishop with a conscience would allow that to happen. They are fulfilling their duty to the Catholic Faith of the Ages before God.

The Society doesn't want regularization, so, even if Rome offered it unconditionally they will not accept it b/c they do not want to lose their autonomy. They wish to operate apart from the Church with their own distinct institutions. So, they say abstractly that they recognize the headship of the Pope but in practicality they operate independent of even his legitimate authority. I can no longer support this, and no longer attend their chapel Masses. I will just drive a little further to assist at a diocean TLM.

@philosopher You said "the Society doesn't want regularization". That is a patently false statement that is plainly contradicted by the facts on the record. The SSPX has been requesting to meet with the Holy Father for seven (7) years. That's what Catholics "who want regularization" do....request a meeting with the Holy Father.
When Rome's only answer is that SSPX cannot have Bishops to care for the over half-a-million Catholic souls in their care, to perform the thousands of Confirmations for their children, ordain their Seminarians and ensure the preservation of the Traditions they have received from Holy Mother Church of the Ages, it is proof that IT'S ROME WHO DOES NOT WANT SSPX REGULARIZED, AND ROME WILL DO EVERYTHING TO STOP IT. NOTHING COULD BE MORE OBVIOUS.

Why walk away from dialogue with the CDF? Tucho is bad but his office must be respected. The CDF is directly under the Pope and reports to him. Pope Benedict did this also. He first had Bishop Felley have discussions with Cld. Muller head of the CDF before meeting with him in person. Try and sell it to someone else, I'm not buying it.
A Cistersion Abbott in France wrote the SSPX a letter asking them to work with the CDF and go back to the May 5th 1988, statements of Archbishop Lefevbre who said he would agree to signing a document acquiescing to that Vat II was valid and could be interpreted in light of tradition albeit open to criticisms, that the Novus Ordo was also valid. The holy Abbot who celebrates the TLM at the monastery in France, never got a response from the SSPX -they just ignored him. As I have said before, they don't want regularization b/c they want to remain in control of their institutions, do not trust Rome, and do not consider them legitimate successors of the Apostolic Tradition.

@philosopher Why walk away from dialogue with CDF? First, because as a precondition, Rome stated the SSPX could not have Bishops, so it was just about running out the clock, not negotiations on how it could be arranged. That's evil. Second, for the same reason Eve should have walked away from dialogue with satan. It's complicity in their subterfuge.

No schismatic has ever had the intention to do a schismatic act. They always intended to "preserve the true faith". It is not the intention that counts but the act itself. God will judge the intentions....

I'd say the Modernists/Globalists want a schism and they want the blame on someone else. Pope Bergoglio tried and failed. Bergoglio acted like a heretic before he was pope.