Because of how it can be tied it to experience.
You find the same dynamic at play whether in the words of the Bible itself, in sermons being preached, in studies on theology, or just in conversations between Christians: Part of what’s written or said touches real human experience, while the rest frames and interprets that experience into a narrative—a story that accounts for it.
When I was 17, I started dating this Christian girl. She took me to a church concert. I don’t remember much, but something the singer said really stuck with me: basically, “You can’t do it alone; you can’t carry your spiritual burden alone; you can’t change alone. You need Jesus.”
At the time, I was working hard to better myself; but I always had this underlying sense of falling short. That was the experience the Christian singer’s comment tied to. Needing Jesus was the accounting narrative.
That same two-pronged dynamic—experience and accounting—is so easy to point out in every case that I don’t actually think nonbelievers ever have to argue against believers directly. An honest nonbeliever need only repeat back exactly what the believer believes and why, and then say sincerely, “I think I see why you believe that; I just don’t believe the story behind it.”
Yes, Christianity is tricky because it makes believing the story its whole foundation and currency. But that doesn’t matter, since the story never touches experience directly . . . it’s just used to explain it.
Since you asked why the Bible is thought to be special, I’ll say this: The great thing about a religious system that expresses and accounts for experience is it can serve as an effective proxy for believers to dig deep into their real life issues, desires, etc.
Here are three practical ways the biblical proxy system helps Christians live better lives:
Purpose: Our innate desire to build value somewhere in the world is shown and framed by such verses as:
For we are God’s masterpiece. He has created us anew in Christ Jesus, so we can do the good things he planned for us long ago. (Eph 2:10)
“I know what I’m doing,” says the LORD. I have it all planned out—plans to take care of you, not abandon you, plans to give you the future you hope for.” (Jer. 29:11)
Conscience/Character: Paul literally equates our conscience to God’s voice (Rom. 2:15, Gal 5:19-23). That’s a great example of the two prongs—experience accounted for by a story. You experience your conscience; the narrative says that’s God talking to you.
Here’s a verse that touches our desire to grow and mature:
When troubles of any kind come your way, consider it an opportunity for great joy. For you know that when your faith is tested, your endurance has a chance to grow. So let it grow, for when your endurance is fully developed, you will be perfect and complete, needing nothing. (Jam. 1:2-4)
The third benefit I’ll mention is a little more complicated.
Within and since the Bible, we see perspectives developing and adapting—perspectives on God, morality, culture, etc. Whenever God’s people are in power, the focus is on social order, rank, and conquest. But when God’s people are disempowered, the call is to personal repentance and social awareness. The Old Testament prophets and Jesus are great examples of the latter.
If the Bible and Christian traditions can be seen as the evolving conversation/perspectives they are, then it seems they can be mapped to social evolution—to love and altruism supplanting greed and power as some of our highest ideals.