How can you read church history and walk away with the conclusion that the Roman bishop and his church are infallible?
The Bible is Infallible. However, the Bible is not the only Infallibile authority in Christianity.
The Church is also an Infallibile authority in Christianity. As a matter of fact, Jesus Christ gave authority to the Church to forgive and retain sins, to bind and to lose, to make disciples of all nations and to even solve individual problems.
Christ Himself told us:If you can’t settle a conflict between yourselves, take it to the church (Matthew 18:15-17).
He didn’t say "go open your Bible in private and find a verse to weaponize."
He pointed us to the gathered body of believers; accountable, relational, Spirit-led community.
St. Paul called the church the Pillar and Bulwark of the Truth. (Timothy 3:15)
All these also imply that the best place you'll get the best explanation on the Bible is the Church. Your personal interpretation can be fine, but not perfect
While Protestants may have their own opinion, you cannot change the truth.
The Catholic Church agrees that the Bible is an Infallibile authority. However, the also Church affirms strongly that the Church is also an Infallibile authority.