That's why I'm a Calvinist.
Luther, Calvin, Wesley, Pope Leo X, Pope Pius XII and Pope John Paul II are all men, fallible and fallen.
Christ is the only infallibility; God's grace our only salvation.
Don't you see the problem here? When you read the bible, you are just as prone as anyone else to error. You a fallen, fallible man, read the bible and then you say "Aha! I have found the infallible truth!" How do you KNOW you have not made an error? How?? You are just a fallible man like the rest. So why should I pay a bit of attention to what you say the bible says?
The whole idea of private judgement is irrational. It does not work. It has not worked. It will never work. You say you trust only in Christ, but it is YOU who is doing the trusting, and you are fallible. So how can you know that you are really trusting Christ and not letting your own will interfere? You don't know. If a teaching is not infallible, then I say, the hell with it.