A reaction of this kind is usually a product of negative volition and the response of one who has not been prepared by the Holy Spirit—but your witness may be part of the way the Spirit will help prepare them. Nevertheless, we do need to be able to answer genuine questions with good answers that will challenge such responses which are often just a way to avoid responsibility to God. Behind them is often nothing more than an attempt to avoid having to face the light of truth.
If you are in a position where you can open your Bible or even quote from it, one way to handle this is to simply use key verses like John 14:6, Acts 4:12 and then ask, “What do you think Jesus meant when He said, “I am the way the truth and the life, no one comes to the Father except through me.” Or, in the book of Acts, the apostle Peter who saw the risen Christ along with more than five hundred other brethren (1 Cor. 15) said of Him, “And there is salvation in no one else, for there is no other name under heaven given among people by which we must be saved.” Then ask, “Just what do you think Peter meant by this? How else can you interpret this?” This gives them the truth and puts them in a position where they have to deal with the plain statements of Scripture.
Other good questions that causes people to think about what they believe or don’t are: Do you have any kind of spiritual belief? What’s the basis for your belief? Who is Jesus to you? If what you believe is not true, would you want to know? If yes, then share the gospel by using your Bible.
Here are some resources that can help fortify you with answers:
Rebecca Pippert has an update on her excellent book, Out of the Salt Shaker and into the World. It deals with the mindset of our present generation.
Erwin Lutzer’s, Christ Among Other gods and How You Can Be sure That You Will Spend Eternity With God. Both of these are wonderful books. I highly recommend them.
Lee Strobel’s, The Case For Christ is also another great book.