He was declared to be a heretic. Period. Furthermore, infallibility/supremacy was an unknown and foreign concept at the time.
**In order for the case of Honorius to disprove the doctrine of papal infallibility as defined by the First Vatican Council, it is not sufficient to claim the pope was a monothelite. It must be demonstrated the pope taught heresy within the parameters of Vatican I.
the actual required conditions are twofold: The pope must exercise his office as “teacher of all Christians, in virtue of his supreme apostolic authority,” and he must define a doctrine concerning faith or morals to be “held by the whole Church” (First Dogmatic Constitution on the Church of Christ, iv, quoted in The Church Teaches, John F. Clarkson, S.J. et. al, ed., 102).
Not every exercise of a pope’s primacy involves his office and authority as “teacher of all Christians.” This primacy also includes—in addition to the power to teach—the power to rule and govern the whole Church. The truth is, a pope can exercise his supreme authority in any number of ways without involving the gift of infallibility—appointing and deposing bishops, suppressing religious orders, altering or imposing disciplines, etc.
Sergius wrote to Honorius to obtain not a dogmatic teaching but a rule of silence that Sergius misrepresented as necessary to end needless wrangling over disputed expressions. Honorius, without further investigation, accepted Sergius’s presentation at face value, seeing the dispute as “an idle question” to be left to the “grammarians who sell formulae of their own invention” (Scripta fraternitatis vestrae**, quoted by Fernand Hayward in A History of the Popes, 90). It is no surprise, therefore, that Honorius wrote that “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” (*Scripta dilectissimi filii *quoted by William Shaw Kerr in *A Handbook on the Papacy *196; emphasis added).
These words make it clear Honorius did not address the nascent heresy as the “teacher of all Christians” defining what ought to be believed. On the contrary, the pope declines to “define” anything and merely follows Sergius’s suggestion in saying neither expression should be spoken of. Whether Honorius’ letters later “affected the whole Church” is immaterial to the question of infallibility.
The proper question is whether Honorius proclaimed a doctrine to be “held by the whole Church.” The answer to this question is clearly “No.” Honorius urged a rule of silence, not a rule of faith. His letters, which anathematized nothing, were intended for a few Eastern bishops and were unknown in the West until after his death. They were hardly the sort of documents with which a pope communicates his intent to bind the whole Church to a solemn dogmatic definition. Unfortunately, the unintended consequence of Honorius’s policy was to leave the monothelite patriarchs in the East in place.
Papal infallibility does not mean the bishops of Rome will be holy, wise, or as vigilant as they ought to be in the discharge of their office. While Honorius’s foresight, as well as his vigilance to his pastoral responsibilities, might be faulted, these are not objects of papal infallibility. Neither is a failure to teach—the doctrine applies only to what is taught. Consequently, the case of Honorius provides no proof against this Catholic dogma. On the contrary, the history of monothelitism and the Sixth Ecumenical Council provides striking evidence of the early Church’s acceptance of the primacy and infallible magisterium of the apostolic see.