The Vatican does not refer to them as schematic.
What do you think of the following argument:
Premise 1. A person or a group becomes a schismatic by committing either (A) or (B) below, or both.
(A) Refusal to submit to the commands of the Supreme Pontiff.
(B) Refusal to associate with those who are subject to the Supreme Pontiff.
Premise 2. The SSPX commits at least one of the above. (Actually, I think they commit both, but this argument only requires one.)
Conclusion. Therefore, the SSPX is schismatic.
Do you think that is a valid argument?
Here is why I think Premise 2 is true:
I think the SSPX rejects some of the teachings of the Second Vatican Council, and I think the popes have commanded us to accept those teachings. Also, I think the SSPX rejects the New Mass as a bad thing, and I think the popes have commanded us to accept it as a positive good. Also, because I think they reject the New Mass, I think they refuse to associate with New Mass attendees, except if the New Mass attendees go to an SSPX Mass. Since I think all these things are true, I think the SSPX fulfills conditions A and B together, and I think fulfilling even one of those conditions would make a person schismatic.
I hope that clarifies my meaning.
I agree they are not anti-Catholic at all and to say so is bearing false witness unless the accuser can provide proof.
What do you think of this argument?
Premise 1. Whoever tries to get Catholics to reject the New Mass or any teaching of the Second Vatican Council is anti-Catholic.
Premise 2. The SSPX does at least one of those things. (Again, I think they do both, but this argument only requires one.)
Conclusion. Therefore, the SSPX is anti-Catholic.
Do you think that is a valid argument?