The Bible is the Word of God and therefore carries with it divine authority. It is binding upon every man, whether he admits it or not, and it is the ultimate standard for our mind, conscience, will, and heart. The reason for this is because it is truth, and it is God's Word, and it is right. That is exactly what the word infallible means, "right", or "perfect". God is God, and He Knows everything, and He has spoken, and it is right, and we must submit. That is the essence of the word infallible.

Ps 19:7-11 7 The law of the LORD is perfect, converting the soul; the testimony of the LORD is sure, making wise the simple; 8 The statutes of the LORD are right, rejoicing the heart; the commandment of the LORD is pure, enlightening the eyes; 9 The fear of the LORD is clean, enduring forever; the judgments of the LORD are true and righteous altogether. 10 More to be desired are they than gold, yea, than much fine gold; sweeter also than honey and the honeycomb. 11

Moreover by them Your servant is warned, and in keeping them there is great reward.