Another poster used the word credibility, and that better fits where I’m at than the word authority. I like the test offered by the Vincentian Canon:
“The famous threefold test of Catholic orthodoxy expressed by St. Vincent of Lérins (400-50) in his two memoranda (Comonitoria): “Care must especially be had that that be held which was believed everywhere [ubique], always [semper], and by all [ab omnibus].” By this triple norm of diffusion, endurance, and universality, a Christian can distinguish religious truth from error.”
Georg Calixtus, a 17th century Lutheran theologian, argued for what he called the concensus of the first five centuries, that being a period in which Christians were by and large undivided. The canons of the Anglican church included this statement:
“See to it that you teach nothing. . .which you would have religiously held and believed by the people, save what is agreeable to the teaching of the Old or New Testament, and what the Catholic fathers and ancient bishops have collected from this self-same doctrine.”
Doctrinal innovations that appeared later only within the Roman Catholic Church, those not held by the Orthodox, Anglicans, and other Christian bodies, seem far less credible to me: priestly celibacy, various beliefs about the pope and Mary, purgatory, indulgences, etc. I have no authority to refer you to to convince you that the Roman Catholic teachings are in error; I can only say that I don’t believe them, and that’s a reason I reject the Pope’s authority.