People often wonder why finite sin deserves infinite punishment, but they shy away from that logic as they try to squeeze through the gates of heaven. We must also ask: why do finite good deeds require an eternal reward? It's impossible to accumulate enough good works to gain eternal life. I suppose God's justice might be satisfied if the afterlife consisted of 80-100 years of paradise. But since the soul is an immortal being, we can't merit the type of reward that God wants to give us.
Paul asks some important questions when he says this:
But the righteousness based on faith says, "Do not say in your heart, 'Who will ascend into heaven?'" (that is, to bring Christ down) or "'Who will descend into the abyss?'" (that is, to bring Christ up from the dead). (Romans 10:6-7)
The point is that we can do nothing to gain eternal life, which is why God did it all. But it's not as if we play no role at all in our salvation. Paul is quoting the Law which says this:
For this commandment that I command you today is not too hard for you, neither is it far off. It is not in heaven, that you should say, 'Who will ascend to heaven for us and bring it to us, that we may hear it and do it?' Neither is it beyond the sea, that you should say, 'Who will go over the sea for us and bring it to us, that we may hear it and do it?' But the word is very near you. It is in your mouth and in your heart, so that you can do it. (Deuteronomy 30:11-14)
This Scripture makes perfect sense when we read "the word" as Christ. As important as good deeds are to the Christian lifestyle, they don't save us. But God has done that for us, so that we now have the ability to merit salvation through Christ.
I suppose it isn't necessary to throw Scripture at your friend. The point I'm trying to make is that those who believe that good unbelievers don't deserve hell are faced with a difficult question: why should a finite number of good deeds merit an infinite reward? Personally I think the Gospel makes more sense.