In spite of the vast preponderance of evidence that the Bible is accurate, that Jesus is a real person, and that the Resurrection is factual, some people just won't believe. Why would anybody, when faced with the facts, deny them? It is rather frustrating to those who have a scientific nature or a intellectual bent. Logically, if I teach somebody something that can save their life, they will modify their behavior in such a fashion so as to preserve their existence. In practice, people do not do that which is in their own best interest. Why?
I recently read a book called, "The Sixty-Second Motivator." In it, physical therapist Jim Johnson did research to learn how to motivate his patients to reach the goals their physicians had set. Participation is critical to recovery, but some folks just wouldn't do what the doctor ordered. Johnson felt that if a doctor declared something to be important, that should make it important to the patient, but in practice certain personalities do not respond that way. Johnson learned that the goal must be made important to people in their own minds.
Mr. Johnson came up with two basic principles which he called "secrets". "Secret #1" is to "increase importance...Increasing the importance of changing a behavior creates more motivation. More motivation helps you move faster through the stages of change." C. S. Lewis, Josh McDowell, and Lee Strobel all felt it was very, very important to disprove Christianity. They all were initially atheists or agnostics. Mr. Strobel was dismayed when his wife became a Christian, and set out to prove Christians wrong and rescue her from the "dangerous cult." As you know, by the time they finished their investigations to discredit Jesus, they ended up as followers of Jesus and set themselves to sharing the Gospel. If an atheist or an agnostic claims Christianity is false, they should consider it important enough to disprove and do some research. Let them come to their own conclusions.
But what good are goals if people don't think they can reach them? "Secret #2" is to "Increase confidence...Increasing your confidence that you can change a behavior creates more motivation." Some people do not believe they have the intellectual capacity for research. In that case, I suggest reading something short like C. S. Lewis's "Mere Christianity," Josh McDowell's "More Than a Carpenter," or Lee Strobel's "The Case for Christ." Any of these books will give a starting place and get them to thinking. It will also show them how "average Joes" can wrap their heads around difficult concepts.
But back to the basic of why some people simply choose to disbelieve. When I was stationed in Turkey in the early 1990's, I read an article citing an interesting study of people who advocate gun control. It turns out they are motivated by fear. Those who do not trust themselves with firearms feel that, since they cannot be trusted, nobody can be trusted. Fear of God is what motivates the atheist and the agnostic as well, but not in the biblical sense. When confronted with the possibility that they are wrong, they would rather turn a blind eye than recognize the fact that they will be held accountable for their actions, as they have earned punishment.
Biblical fear of God is borne of respect, like respect for authority, not a timorous fear, like the fear of an armed rapist. Read the Gospels. God is not going to "smite" you. You can be forgiven. You are loved. It's safe to believe.