Time and time again, the Bible references eternal flames and everlasting punishment. Matthew 25:46 is one reference: The wicked will go away into eternal punishment, but the righteous into eternal life. It is very clear throughout scripture what that eternal punishment is. It is not death, but an eternity in hell.
Punishment in hell is often defined by the word aionios, which is the word eternal or everlasting. The same word is used to describe heaven, God, and punishment in hell. It doesn't make sense to accept that God and heaven are eternal, but not accept that punishment in hell is eternal. Scripture after scripture talks about eternal punishment in a place where there is weeping and gnashing of teeth (Matthew 8:12) in a fiery furnace (Matthew 13:42, 50) of unquenchable fires. If there is not an everlasting hell, then there is not an everlasting God or heaven.
Matthew 7:13 doesn't say eternal when talking about the narrow gate that leads to life either. But we both would agree that life in heaven is eternal right?
Luke 16:19-30 is another good example. Two men died. One went to heaven while one went to Hades. In verse 24, the rich man says, " I am in tormented in this fire. That is talking about a man who already died. (John 5:28-29) Do not be amazed at this, for a time is coming when all who are in their graves will hear his voice 29 and come outóthose who have done what is good will rise to live, and those who have done what is evil will rise to be condemned.
Why is God going to call those who have done evil out of their graves ("literal" death) just to condemn them back to a literal death? That doesn't make sense, and it doesn't go along with the Bible's descriptions of hell and eternal punishment.
I think what it comes down to is us not wanting to believe the Bibleís teaching about eternal torment. It is a scary doctrine. Itís impossible for us to conceive of us doing something so bad that merits everlasting torment described in the Bible. It is a lot easier to just think that we cease to exist. However, that just goes to show just how little we understand about the holiness of God and how seriously he takes sin.