Scripture itself claims to be infallible:
“If he called them gods, to whom the word of God came (and the Scripture cannot be broken)…” (Jn 10:35)
So if this statement is fallible, I don’t know how we can tell what parts are not fallible.
“In the late 1940s, Billy attended a conference in California only weeks before his largest crusade to date was to start. Some young theologians were also there, who were expressing their doubts about the authority of the Bible. ‘Suddenly, I wondered if the Bible could be trusted completely.’ Billy began to study the subject intensively, turning to the Scriptures themselves for guidance. ‘The Apostle Paul,’ Billy said, ‘had written to Timothy saying, “All Scripture is given by inspiration of God.” Jesus himself had said, “Heaven and earth shall pass away, but my Word shall not pass away.” I thought also of Christ’s own attitude, He loved the Scriptures, quoted from them constantly, and never once intimated that they might be false.’ Billy then recalled the moment that changed him forever. ‘That night, I walked out in the moonlight, my heart heavy and burdened. I dropped to my knees and opened my Bible on a tree stump. If the issue were not settled soon, I knew I could not go on. “Oh God,” I prayed, “There are many things in this Book I do not understand. But God, I am going to accept this Book as Your Word by faith. I’m going to allow my faith to go beyond my intellect and believe that this is Your Inspired Word.” From that moment on I have never doubted God’s Word. When I quote the Bible, I believe I am quoting the very Word of God and there’s an extra power in it. One month later, we began the Los Angeles crusade.’ ” (Billy Graham)
AC 2:37 When the people heard this, they were cut to the heart and said to Peter and the other apostles, “Brothers, what shall we do?”
“I have had the privilege of preaching this Gospel on every continent in most of the countries of the world. And I have found that when I present the simple message of the Gospel of Jesus Christ, with authority, quoting the very Word of God—He takes that message and drives it supernaturally into the human heart.” (Billy Graham)