Honorius was condemned in the sixth General Council in 680 not because he actually taught heresy, but because he was negligent and did not do his duty to stop the spread of the Monothelite heresy. This does not disprove papal infallibility, because Honorius did not teach it as infallible truth or dogma nor did he bind the Church to this teaching. Infallibility logically implies that you actually teach it and bind the Church to it.
Your logic is intermittent.
The case of Pope Honorius I is not as simple as it seems to those who argue against papl infallibility on matters of faith and morals. Honorius was pope from 625 to 638 A.D. During his pontificate, the patriarch of Constantinople, Sergius, fell prey to the Monothelite heresy, the belief that in Christ there is only one will. Sergius wrote a letter to Honorius, asking whether Christ had one “operation” or two. Sergius used obscure and confusing language. Honorius reponded by condemning both expressions, one operation or two operations. The problem with the blanket condemnation is that the expression, two operations, can be interpreted as orthodox. John Symponus, the man who composed Honorius’s letter, said that Honorius only meant to condemn the idea that Christ had two contrary wills. Nevertheless, Honorius’s confusing letter was used by many to buttress the heretical Monothelite position. The Sixth Council–at Constantinople–condemned the Monothelite heresy, along with those who held it. Honorius was one of those declared anathema, but this was without the approval of Pope Agatho. Agatho’s successor, Pope Leo II, confirmed the council’s decree but clarified its language regarding Pope Honorius, making it clear that Honorius had not endorsed the Monothelitism of Sergius, but had failed in his duty to condemn it. Officially, Honorius was condemned for his negligence, not for heresy. It should be noted that the council took place more than 40 years after the death of Honorius.
Pope Honorius was in point of fact condemned as a heretic. There is an identical discussion underway on this on another thread
When the Church declares someone to be anathema after their death, this tells us that the person in question never renounced their heresy, never repented of it, and therefore died in a state of separation from God, as an apostate, outside of the Church and her graces.
But if he never formally said he believed it then there would be no reason to repent for a heresy.
Where could I find more information on these two things?
You can start with the book, *Pope Fiction, *by Patrick Madrid. Also, you can read the articles in the Catholic Encyclopedia on Popes Honorius I, Agatho, and Leo II. There’s also an article on the 6th Council at Constantinople. The Encyclopedia can be found at www.newadvent.org.