Papal Infallibility
The doctrine of papal infallibility was not new and had been used by Pope Pius in defining as dogma, in 1854, the Immaculate Conception of Mary, the mother of Jesus. However, the proposal to define papal infallibility itself as dogma met with resistance, not because of doubts about the substance of the proposed definition, but because some considered it inopportune to take that step at that time. McBrien divides the bishops attending Vatican I into three groups. The first group, which McBrien calls the "active infallibilists", was led by Manning and Senestrey. This group took an extreme view that argued that all papal teachings were infallible and that papal infallibility was the foundation of the church's infallibility. According to McBrien, the majority of the bishops were not so much interested in a formal definition of papal infallibility as they were in strengthening papal authority and, because of this, were willing to accept the agenda of the infallibilists. A minority, some 20 percent of the bishops, opposed the proposed definition of papal infallibility on both ecclesiastical and pragmatic grounds. They opposed the ultramontane centralist model of the Church because, in their opinion, it departed from the ecclesiastical structure of the early Christian church. From a pragmatic perspective, they feared that defining papal infallibility would alienate some Catholics, create new difficulties for union with non-Catholics, and provoke interference by governments in Church affairs. Those who held this view included most of the German and Austro-Hungarian bishops, nearly half of the Americans, one third of the French, most of the Chaldaeans and Melkites, and a few Armenians. Only a few bishops appear to have had doubts about the dogma itself.
Read more about this topic: First Vatican Council