Final answer:
Pope Honorius's reply to the Patriarch of Constantinople does not meet the test of papal infallibility because it contradicted previous teachings of the Church regarding the nature of Jesus Christ's wills.
Step-by-step explanation:
The claim of papal infallibility is that the Pope, when speaking on matters of faith and morals ex cathedra (from the chair of Peter), is protected from error by the Holy Spirit. However, Pope Honorius's reply to the Patriarch of Constantinople did not meet the test of papal infallibility because it contradicted previous teachings of the Church. Honorius was accused of supporting the monothelite heresy, which denied the existence of two wills in Jesus Christ (divine and human). His reply to the Patriarch seemed to support this heresy, going against the established faith and teachings of the Church.