When the Bible speaks of the "world" being destroyed it is talking about mankind, specifically wicked man, not the literal earth. That is where people get mixed up. The Bible says Jehovah God created this world to be inhabited, he didn't create it for nothing. (Isaiah 45:18) In Noah's day it was the "ungodly men" that were destroyed; as you can see the earth is still here. (2 Peter 3:7)
When it comes to the issue of the authenticity of the Bible, if you look at the scripture at 1 Timothy 3:16 it lets us know that all scripture is inspired of God. Many discount the Bible and what it says, and these are the very same ones that haven't even cracked one open or have read a little bit and claim they already know all of its contents. They read a little and feel they have the right to say it has nothing important for us.
The Bible actually has in it the issue that was debated many years ago, the issue of shape of the earth. It had this long before this even became an issue. Isaiah 40:22 tells us that the earth is a circle. So the Bible had to be inspired by someone who knew the shape of the earth. No human could tell for many years.
Also there are prophesies that are foretold in the Bible that have already been fulfilled. Humans can't predict exactly what is going to happen to humans as a whole. There is only one person that can do this. One of those prophesies we see being fulfilled today. The one at 2 Timothy 3:1-5 where it tells us "that in the last days critical times hard to deal with will be here. For men will be lovers of themselves lovers of money...haughty...disobedient to parents...betrayers, headstrong, puffed up with pride, lovers of pleasure rather than lovers of God, having a form of godly devotion but proving false to its power." You have to agree that we see all of this and then some.