[Cronos]

Simply put, papal infallibility is thanks to the grace of the Holy Spirit when

1. the Pope solemnly declares i.e. TEACHES
3. a teaching on faith or morals as being contained in divine revelation, or at least being intimately connected to divine revelation, he, under the Holy Spirit's protection is preserved from even the possibility of theological, dogmatic error.
   
   Pope Honorius did NOT teach Monothelitism in any way, as a solemn teaching to the Church.
   
   Honorius' failing was that he did not condemn the followers of Monothelitism --> he basically said "let's keep quiet and not support either side as that will only cause mischeif"("on account of the simplicity of man and to avoid controversies, we must, as I have already said, define neither one nor two operations in the mediator between God and man"
   
   Hence there is no question of Honorius' papal infallibility
   
   The council rightly ANATHEMIZED Honorius because Honorius failed to be a bishop and teach against the heresy

[RnMomof7]

Simply put, papal infallibility is thanks to the grace of the Holy Spirit when

And Christ told them they could pass on the special gifts He gave for the foundation of the New Testament church where again?
Scripture teaches peters infallibility where again?

[OLD REGGIE]

Simply put, papal infallibility is thanks to the grace of the Holy Spirit when

1.the Pope solemnly declares i.e. TEACHES
2.
3.a teaching on faith or morals as being contained in divine revelation, or at least being intimately connected to divine revelation, he, under the Holy Spirit's protection is preserved from even the possibility of theological, dogmatic error.

I'll go with number 2. (To be determined as required.)

The Sixth Ecumenical Council infallibly found Honorius guilty of Heresy and Excommunicated him.

The Catholic Church has a unique practice of "Retroactive Definition" in order to explain away past practice.

By his letters Honorius taught error.