One non-Christian I spoke with, a Unitarian, once said to me "No one has shown me anything that proves the Bible is more valid than any other holy book." When I persisted he said, "How would you feel if a Muslim friend kept telling you that your soul was damned to hell if you didn't follow the Qur'an?" How do I argue against that?
My first response would have been, "Ah! So you don't believe the Bible." You see, the Bible does claim to be more than any other religion. It claims to contain words from the mouth of God. "All Scripture is given by inspiration of God" (II Timothy 3:16). The phrase literally means all the sacred writings are breathed from the mouth of God.
The Bible is filled with evidence that it is the work of God. I don't have time to make a complete listing as it would require writing a book, and several have been written on the subject. However, let me recommend reading over the material filed under the topic of Apologetics as a start.
God challenged people to present their case supporting their gods against Him. ""Present your case," says the LORD. "Bring forth your strong reasons," says the King of Jacob. "Let them bring forth and show us what will happen; Let them show the former things, what they were, That we may consider them, And know the latter end of them; Or declare to us things to come. Show the things that are to come hereafter, That we may know that you are gods; Yes, do good or do evil, That we may be dismayed and see it together"" (Isaiah 42:21-23). One of the strong evidence given in the Bible is the fulfillment of prophecy. No other religion has solid evidence that is recorded in the Bible. Other religious books show flaws and internal contradictions, but the Bible has stood the test of time. Hence, God concludes, "Indeed you are nothing, And your work is nothing; He who chooses you is an abomination" (Isaiah 42:24).
Actually, the Qur'an both supports and rejects Christianity. Its inconsistent stand on the salvation of Christians makes for interesting discussions. A person may express their belief, but I have the same right to tell them why their belief does not match the teachings of God. As a Christian, I have no reluctance standing behind the teachings of the Bible because I know they are vastly superior to the works of men.