This "logic" is Donatism, which was condemned by the Church in the 3rd and 4th centuries, and is itself heretical.
It violates reason, since it ignores the difference between infallibility and impeccability. It is unjust, because it rhetorically universalizes non-universal faults of individuals and institutional components, and imputes them to the whole.
Most importantly, it makes a liar of Christ, which is why I cannot accept it. Sedevacantism will be the ruin of souls.
Keep in mind this maxim by St. Francis de Sales: "Those who give scandal commit spiritual murder; those who take scandal -- who allow scandals to destroy their Faith -- commit spiritual suicide."
Thank-you for your help!
Sedevacantist chapels are alive and well and more springing up all the time.