There are a few aspects of Calvinist justifications for the doctrine of hell that deserve to be elaborated. First, Calvinists think we need to kneel before our creator and submit out moral judgments, or, as they like to say, intuitions, to Scripture. Scripture, they claim, is inerrant, and teaches both predestination and the doctrine of hell. There's an exegetical catfight involved in the Calvinist debate. They offer exegeses if 2 Pet 3:9, John 3:16, and a host of other verses which are consistent with Calvinism. Opponents of Calvinism offer explanations of Eph 1:12, Romans 9, etc.
By they way, I do not think universalism is a nonstarter from a biblical perspective. I think Tom Talbott and other evangelical universalists have a case. Maybe not a winning case, but a case.
But a mere appeal to Scripture will not provide us with elucidation or explanation as to why God might do this. Lewis's Great Divorce defense of hell makes hell at least somewhat understandable, but it requires us to have libertarian free will that God must eternally respect.
Calvinists will readily admit that God could save everyone but chooses not to.
Calvinists, so far as I can see, make three moves in defense of reprobation:
1) Hell is what everyone deserves. In fact in federal theology, we can retributively deserve hell because of the actions of Adam. But, setting that aside, we perform sinful actions which fail to give God the glory he merits by being God, and we perform these actions with compatibilist free will. We aren't forced to do them, we want to do them, therefore we do them. OK, we want to do them because God predestined that we should want to do them, but that doesn't matter, we're still guilty and deserving of punishment.
I don't think compatibilist free will is sufficient for retributive punishment, and retributive punishment by the person whose actions guaranteed that the action being punished was performed in the first place strikes me as morally perverse in the extreme. So this response doesn't make hell at all understandable to me, and I don't think my intuitions are idiosyncratic here. So, even if true, this defense doesn't provide any comprehensibility to divine reprobation.
Second, Calvinists argue that the good is ultimately God's glory, and what that amounts to is God's expression of all of his attributes. He has the attribute of lovingness, which he expresses toward the elect, and he has the attribute of wrath, which he exercises toward the lost. If God were to decree universal salvation, he would be impoverishing his own glory, since he would be exercising fewer of his attributes.
But I don't see that it gives God any glory to give him a split personality. When you love, there are certain circumstances under which wrath is an appropriate expression of love. Every parent knows that. Making wrath a separate attribute that requires "expression" in order for God to receive sufficient "glory" makes absolutely no sense to me.
Third, Calvinists argue, using the "vessels of wrath" passage in Romans 9, that God creates reprobates so that the elect can appreciate the graciousness of their own salvation. It's a little bit like the story of young John Wesley's rescue from a burning house. His mother said he was a brand plucked from the burning, and he saw himself as someone with a special mission because of that. But again, I don't see that people who have face-to-face knowledge of God would need eternally suffering object lessons. How this increases the total balance of pleasure over pain in the universe strikes me as completely unclear, and why that would be justified even if we set utiltarianism aside is also completely obscure to me. It is hard to me to think that I am any less of a Christian if, in imagining myself perceiving the sufferings of the predestined reprobate, my first response is "Why couldn't God's grace have been extended to them?" as opposed to "Praise God. There but for the grace of God go I."
Yes, yes I know. Calvinists have responded to these points. Obviously their explanations make sense to them. They make absolutely no sense to me.
So, there is no basis that I can see that makes hell at all understandable, if God could have chosen a universalist world, but didn't.
A final response I have heard is the fact that God could have a reason for reprobating people that as a human I don't understand. After all, any theist has to accept the existence of apparently unredeemed evils. But with temporal evils, we can at least conceive of a future story that redeems those evils. In the case of reprobates, the evils are irreversible. They won't be redeemed in the future history of the world.
Karl Barth once said "Belief cannot argue with non-belief, it can only preach to it." Maybe that's the situation with Calvinism and their opponents.