Trying to witness to an atheist and no matter what I say, how I try to use logic and reasoning, or even recommend books with plenty of defenses of Christianity, or even websites with defenses the atheist become illogical and base their rejection of christian on "bad experiences" or "bad people."
It sounds like your mistake has been to try to reason someone into the Kingdom. It doesn't happen on the basis of reason. It happens through a work of God's Spirit. Now, saying that, it often involves reason, but reason takes a backseat to the Spirit's work.
Because unless God grants repentance and regeneration which proceeds faith they can never come to faith. God knows His elect and has called them to salvation. For them books on evidences of Christianity are valuable. To them to Bible is pure gold. But to others the Bible and everything is worthless and they will never consider it.
Yes, I agree.
As someone who has more than a dozen atheist friends (they seem to be drawn to me), I can tell that they are looking for evidence of the supernatural in my life. If Jesus is Who He said He was, then that is a legitimate test. If I can love them in the midst of their brokenness, can demonstrate intellectual honesty and brutal honesty about faith, can stop worrying about what they think of me, can confront their foolish ideas in an appropriate and loving way, and can see evangelism and apologetics as spiritual assistance and not a game to win, then God is glorified and perhaps they will come to faith as the Spirit leads.
I have seen a few make that journey. Shortly after each one was converted, they were "replaced" with new atheist friends.
Apparently God uses my personality and gifts to do a work in certain hard hearts. Now, there are not too many who have made that leap - I think four in the last 10 years - but it's not my job to keep score, just be faithful
Here's something to throw out to an atheist who demands "proof": Ask them what try of proof they would like to see. Most of the time you will get a blank stare because they suddenly realize that they are actually not open to "proof" at all, at least, they don't even know what they claim to be looking for. That's where you can tell them to figure out what proof/evidence they would like to see before making a huge arrogant claim that there is "no evidence for God."
In the unusual case that they do give you something, rationally walk them through all the reasons why they would/should disbelieve it based on the standards they have previously used. You can then make the point that they probably have inoculated themselves to proof, so why should God do tricks for them. However, if you do actually reach an acceptable proof, enter into prayer with them about it and let them know that God may actually provide it if they are sincere about their openness.
I have used that line of response on a number of occasions and it never fails to underline that the atheist often claims things that they haven't thought through. Moreover, it can set them on a path to humility and intellectual honesty and open up other opportunities to talk. But be ready to be able to provide your evidence - that you have personal knowledge (that is, the knowledge of Persons) that we all experience when we meet someone/Someone. Experience *is* evidence even though it doesn't fit within the scientific method. But using the scientific method to measure *all* things is reductionism of the worst kind.
In short, don't get in a debate with an atheist. Have a conversation. And don't be afraid to stop the conversation if things get a bit heated. Tell then, "I'd rather let you claim victory than for you to lose sight of the fact that I care deeply about you and your welfare as a person." That shifts the point of the conversation from who is right, to who is loved. And they are love passionately by God.