Self refuting statements are extremely common in anti-Christian worldviews. The most obvious example would be Relativism. Relativism is becoming increasingly popular. We are being told that all truth is relative, truth depends entirely on what you believe. What's true for you is true for you, what's true for me is true for me, there are no absolutes. But is that absolutely true?
Relativism is completely unworkable. When you cross the street, a bus is a bus. You need to beware of the bus so it doesn't hit you, you need to beware of the Lord so He doesn't condemn you. The absolute truth is that eventually, you are going to die, and you will face the Lord, who will judge you according to your works. And unfortunately, you have absolutely sinned and fallen short of His glory, meaning you deserve punishment.
The good news, however, is that this is where God offers us a choice. 2,000 years ago, He absolutely came to the earth as a man named Jesus, who absolutely never sinned, and absolutely died upon a cross, and absolutely rose from the grave. Those who repent of their sin, confess Him as Lord, and believe He rose from the dead, will absolutely never be condemned, but will instead absolutely receive eternal life.