Why is it important for a Christian to believe that the Bible is divinely inspired?

First of all, if the Bible is not divinely inspired, then it is nothing more than the writings of men. As such, it is no more the truth than any other writing of man. Every man's idea is as good (or as bad) as every other man's. Thomas Paine's "Age of Reason" which preaches atheism would be as much the truth as the Bible would be.

Second, there would be no source of absolute authority for truth. We have no other source for eternal truth. Since the great truths like the purpose of man and the question of eternity are outside the realm of human discovery, man could never know the truth. We would be eternally condemned to darkness.

Third, the Bible would actually be a pack of lies. The words of the Bible claim to be the words of God. The phrase "Thus saith the Lord" is found 415 times in the Bible. 2 Timothy 3:16All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
See All... states, "All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness." Paul applauds the Thessalonians because they received the word of God from them "not as the word of men, but as it is in truth, the word of God" (1 Thessalonians 2:13For this cause also thank we God without ceasing, because, when ye received the word of God which ye heard of us, ye received it not as the word of men, but as it is in truth, the word of God, which effectually worketh also in you that believe.
See All...). Now, if the Bible is not inspired by God but is simply the words of men, then it is so full of lies as to make it a wicked book.

It is true that some who are hardened against God and His word would agree with all of the above points. But it leaves them without truth in a darkened world. Scripture compares itself to light and I have found it to be so. I hope and pray that you are walking in that light.