Atheists think Hell is a problem, and sure proof that God is the cosmic sadist of whom Antony Flew wrote. In response, Christians have endeavored to redefine their understanding of Hell, as a place freely chosen. I suspect this is motivated in part by the pastoral desire to appeal to liberal atheists, for whom nothing is worse than being made to do something or be somewhere against one’s will; and if Hell is chosen, after all, it can’t be all that bad.
Actually, “redefine” is maybe a bad choice of word, since there’s much to recommend the view as far as it goes. The problem is that it doesn’t go very far , which atheists get, hence their ubiquitous retort that Hell must be empty because, after all, what kind of person would voluntarily choose such a destination.
Hell is, in a sense, chosen, as a logical consequence of one’s actions. But it is not “chosen” the same way that the outcome of falling to one’s death is chosen by virtue of deliberately stepping off a cliff. Rather, it is chosen in the way that imprisonment is the logical consequence of a murder freely committed by a criminal. The criminal doesn’t get to claim that it is unjust for him to be imprisoned because, after all, he doesn’t want to be imprisoned. Murder is punished just because of the nature of murder, and imprisonment is a rationally foreseeable consequence  of that.
This doesn’t change the fact, though, that imprisonment is a sentence passed by an authority against the (yes, disordered and irrational) desires of the prisoner. The gates of the prison are still locked from the outside. Nor does it change the fact that, given the reality of crime, imprisonment of criminals is good, right, proper, and just — not only for the body politic but for the prisoner, as well.
Just so with Hell. Sin just does lead to Hell the way that murder just does lead to prison (although the causal relationship of the latter is clearer because God, unlike the justice system, is infallible and omniscient). It is a rationally foreseeable consequence of freely-chosen evil, justly punished by a legitimate authority for the good of the whole (the entire order of being) and the good for
“Wait, the good of the prisoner?! How can you think prison is a good thing for the prisoner?” Yes, it’s good for the prisoner to be punished. Why? Because the goodness of a thing is defined by its nature. Thus, the goodness of a sandwich and the goodness of a dog differs according to the precise natures of sandwiches and dogs. Where the characteristic excellence of a sandwich is tastiness and nutrition, and the characteristic excellence of a dog is loyalty, obedience, and companionship, good specimens of each will exhibit these characteristics. Likewise, the nature of man is such that he has reason and free will, and thus moral agency: so it is good for man to act freely and good for man to be held accountable, to be rewarded for his good deeds and punished for his wicked ones. Hell, then, is a necessary corollary of human freedom, without which man would be deprived of the very real natural good of accountability for his actions.
“But what kind of just God would allow a person to suffer unimaginably for the relatively minor trespasses he commits?” Think of it this way: think of your life as a debt. It is a debt, after all: God gave it to you at no cost, simply out of sheer gratuity, along with every other gift He has given you. You owe Him everything. If you live your life in perfect, total, Marian obedience to His will, you will only repay the principal. But you’re not Mary. You sin. Sin occurs charges and penalties, and those unpaid (because unpayable) penalties compound over time as they continue unpaid. From the moment of our very first sin, then, our lives are turned upside-down: we are saddled with a debt of justice we cannot possibly repay. 
The debt cannot be repaid. If we are to escape it, it can only be forgiven. Thankfully, our debtor is generous, and will happily eat the cost of both principal and interest and wipe clean our slate. We will enter eternity with a perfect credit score… if we sign on the dotted line.
Why would you not sign on the dotted line? See note  below.
Whatever the reason, if there is no repentance, there can be no forgiveness — and the debt, on death, enters into collection. But since man has no means to repay the debt, the collection is eternal: an unending stripping of spiritual assets from the damned soul, deprivation of every good which would naturally belong to it: the eternal torment of utter negation.Hell isn’t unjust precisely because justice consists in giving every man what is due to him. But man is due punishment for his sin. We should not complain about God’s justice. We should thank Him that He is willing not to subject us to the full extent of it.
“But what kind of loving God would torture someone for eternity just for picking his nose (or whatever)?” You mistake love, which is simply the willing of another’s good — and man’s goods, as I explained above, include his moral accountability. In other words, Hell exists not despite God’s love but because of it, because, without it, man’s moral responsibility is a myth, and he is denied a good that is central to his nature.
“But isn’t damnation a defeat for God, who desires glorification above all things?” Why do you think the damned don’t glorify God? Are you foolish enough to think that glorification is merely an act — a thing you say or do or dance — and not a state of being? Remember your Scriptures: “[man] is the image and glory of God” (1 Cor. 11:7). Carve that line on your heart: you are the glory of God. God alone could create life, animate it, sustain it: God alone could endow it with the gifts of reason and free will: God alone could create a thing worthy of praise. Everything you do glorifies Him: every second you sleep, every bite of cereal you take, every tear you shed, every groan you issue in the passion of the marital embrace, every second of backbreaking physical labor. Everything. All of it. Do you not have a sense, just looking at the newborn sleeping in your wife’s arms, that the life itself is a miracle? Then you dimly know a fraction of the glory God experiences when He beholds you.
The souls in Hell glorify Him just as much as the souls in Heaven. Even in their agony, they are a testament to God’s awesome creative power and all-encompassing love, for He alone could create a thing that can be punished justly.
I suspect, by the way, that the damned are assisted by God with the graces necessary to understand and experience their punishments as just. Thus the souls huddled on the shores of Acheron in the third canto of Dante’s Inferno experienced neither confusion nor outrage: they were eager to cross over the river to begin their punishments. So Virgil tells the poet: “Divine Justice transforms and spurs them so their dread turns wish: they yearn for what they fear.”
“It all just sounds so… abominable to me. God sounds like a monster.” That’s because you want to be free of moral responsibility. You resent the burden of accountability, integrity, and moral agency, and you resent Him who made you that way. You want comfort and pleasantness above all things, and you would sacrifice your humanity to get it. Whatever else it is you want, you want to be not-a-person.
And that’s just what Hell is — the self-willed obliteration of your own humanity. Wake up and smell the brimstone.
 In a similar way, it’s meaningful to talk about God as both the father of mankind and also the spouse of His Church. Both terms are appropriate in their right contexts, and both capture some of the reality of the relation of man to God; but neither capture that reality in its fullness, so it would be ludicrous for one to accuse God of incest.
 Note those words: rationally foreseeable. When we ask, then, what kind of person would choose Hell, we get a perfect definition of both sin and sinner: an irrational act committed by a person in thrall to irrational modes of thought.
 And note that it is not God’s arbitrary will that makes it so. If God created all things, and if creation incurs automatically a debt of gratitude and obedience, then it could be otherwise if, and only if, God could create an uncreated thing — an ontological impossibility. Therefore, it cannot possibly be otherwise.