Many misunderstand Christianity because they have never actually heard the gospel, or they grew up in a legalistic church that was all about rules. They could be rejecting a wrong understanding of Christianity, not the gospel itself.
One top misconception is that God's grace comes to those who morally outperform others. But the gospel is that God's grace comes to those who admit their imperfections and failure, and know they need a Savior (Tim Keller, The Reason for God, p. 19).
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Some other questions Tim Keller addresses:
How could a good God allow suffering?
Is Christianity repressive (a straitjacket)?
How can a loving God send people to hell?
Has science disproved Christianity?
Isn't the church responsible for a lot of injustice?
Highly recommended best selling resource! Before his death, Keller pastored a church that is thriving and reaching many in Manhattan, that interacts frequently with New Yorkers who are coming from a very different, or even skeptical background, but want to explore faith and learn more about Christ.