The doctrine of Hell is arguably one of the most difficult in orthodox Christianity.
But, for a moment consider Christian doctrine as is, without an infinite Hell.
So what happens when sinners die?
1. Heaven (universalism)
2. Dissolution (Jehovah's Witness)
3. Reincarnation (Hinduism, New Age)
4. Finite Hell (or Purgatory)
1. Universalism destroys the notion of justice. This is saying unrepentant murderers will be with God in Heaven.
2. Dissolution is nearly as bad. Live your life as please, scoff at God, kill and steal, live it up! When you die, it's all over, but you lived as you pleased. No justice here on Earth, and none from God.
3. Reincarnation. This is just a goto 10. I mean, there has to be a last generation. Either when the great and terrible "Day of the Lord" comes, or at the heat death of the universe (for the amillenialists in the audience). And it's not very just in the near term. I should suffer now for the crimes of some person who died around the time I was born? And what if the global population levels off?
4. Finite Hell. This is very attractive. Probably why the Catholic Church was able to sneak Purgatory past people long ago. But there is a problem if you work it all the way through...
What is the payment for sin? (And conversely, what is the damage done by sin?)
If the payment is finite, then it is something we can earn for ourselves. Either doing some things during life, or some hard time in Hell after. But then, our account is all squared up.
So then, why did Christ die? Some sort of horrible mix up? An unnecessary tragedy? To save a few people some hard time in Hell?
And what is God's nature? Is sin a finite transgression against an infinite being? Or is it an infinite transgression? A finite transgression would appear the same as 0 to an infinite being. So really, no one would need to spend more than a few hours in Hell.
Except, God is infinite. And sin is infinitely offensive to Him. And we need an infinite payment. Christ's death paid that. And for those who reject Him, an eternity in Hell will pay it too (at least, approaching it in the limit).