As I read it, Hart is arguing for the following four points (my emphases in bold):
1. The problems thrown up by these catastrophes are not new problems
"...nothing that occurred that day or in the days that followed told us anything about the nature of finite existence of which we were not already entirely aware."
2. Atheists don't understand Christian perspective
"...it is difficult not to be annoyed when a zealous skeptic, eager to be the first to deliver God His long overdue coup de grâce, begins confidently to speak as if believers have never until this moment considered the problem of evil or confronted despair or suffering or death."
"It would have at least been courteous, one would think, if he had made more than a perfunctory effort to ascertain what religious persons actually do believe before presuming to instruct them on what they cannot believe."
(On Voltaire's response to the Lisbon earthquake): "Voltaire’s poem is not a challenge to Christian faith; it inveighs against a variant of the “deist” God, one who has simply ordered the world exactly as it now is, and who balances out all its eventualities in a precise equilibrium between felicity and morality."
3. It is the fault of Christians themselves that they're not understood - lots of bad theology
"In truth, though, confronted by such enormous suffering, Christians have less to fear from the piercing dialectic of the village atheist than they do from the earnestness of certain believers ... more troubling are the attempts of some Christians to rationalize this catastrophe in ways that, however inadvertently, make that argument all at once seem profound."
"All three wished to justify the ways of God to man, to affirm God’s benevolence, to see meaning in the seemingly monstrous randomness of nature’s violence, and to find solace in God’s guiding hand. None seemed to worry that others might think him to be making a fine case for a rejection of God, or of faith in divine goodness. Simply said, there is no more liberating knowledge given us by the gospel — and none in which we should find more comfort — than the knowledge that suffering and death, considered in themselves, have no ultimate meaning at all."
Dostoevsky: "Ivan asks, if you could bring about a universal and final beatitude for all beings by torturing one small child to death, would you think the price acceptable?"
"Voltaire sees only the terrible truth that the actual history of suffering and death is not morally intelligible. Dostoevsky sees — and this bespeaks both his moral genius and his Christian view of reality — that it would be far more terrible if it were."
"No less metaphysically incoherent — though immeasurably more vile — is the suggestion that God requires suffering and death to reveal certain of his attributes (capricious cruelty, perhaps? morbid indifference? a twisted sense of humor?). It is precisely sin, suffering, and death that blind us to God’s true nature."
"...consider the price at which that comfort is purchased: it requires us to believe in and love a God whose good ends will be realized not only in spite of — but entirely by way of — every cruelty, every fortuitous misery, every catastrophe, every betrayal, every sin the world has ever known; it requires us to believe in the eternal spiritual necessity of a child dying an agonizing death from diphtheria, of a young mother ravaged by cancer, of tens of thousands of Asians swallowed in an instant by the sea, of millions murdered in death camps and gulags and forced famines. It seems a strange thing to find peace in a universe rendered morally intelligible at the cost of a God rendered morally loathsome."
4. Suffering is evil, a cosmic disorder, which will be put right (ie mended)
"Ours is, after all, a religion of salvation; our faith is in a God who has come to rescue His creation from the absurdity of sin and the emptiness of death, and so we are permitted to hate these things with a perfect hatred. [SN: ie not try to justify them] For while Christ takes the suffering of his creatures up into his own, it is not because he or they had need of suffering, but because he would not abandon his creatures to the grave."
"As for comfort, when we seek it, I can imagine none greater than the happy knowledge that when I see the death of a child I do not see the face of God, but the face of His enemy. It is not a faith that would necessarily satisfy Ivan Karamazov, but neither is it one that his arguments can defeat: for it has set us free from optimism, and taught us hope instead."
"We can rejoice that we are saved not through the immanent mechanisms of history and nature, but by grace; that God will not unite all of history’s many strands in one great synthesis, but will judge much of history false and damnable; that He will not simply reveal the sublime logic of fallen nature, but will strike off the fetters in which creation languishes; and that, rather than showing us how the tears of a small girl suffering in the dark were necessary for the building of the Kingdom, He will instead raise her up and wipe away all tears from her eyes — and there shall be no more death, nor sorrow, nor crying, nor any more pain, for the former things will have passed away, and He that sits upon the throne will say, “Behold, I make all things new.”
In sum, Hart is arguing that Christian theology does not seek to explain or justify the existence of suffering in the world in terms of God's ultimate purpose. Suffering is understood as a disorder, a privation of the good, something which is opposed to God and which can therefore be 'hated with a perfect hatred'.
Lying behind this article is another perspective that needs to be taken account of in order to understand his argument, about what it means to call God 'good'. Orthodox Christianity is very careful about what it means to call God 'good' because of the ever-present danger of tacitly assuming a place from which to judge God as either good or evil. So when a Christian believer calls God 'good' the language does not function in the same way as it would when such a Christian describes another person as good (or evil), and, further, it becomes just as meaningful to describe God as the source of suffering (of 'weal and woe' as Isaiah puts it) as it would be to describe God as source of good things when those good things are judged as such in human terms.
This is why possibly the most important sentence in Hart's article is this comparatively early one: "Simply said, there is no more liberating knowledge given us by the gospel — and none in which we should find more comfort — than the knowledge that suffering and death, considered in themselves, have no ultimate meaning at all." In other words, the problem of suffering is not as important as we might think it to be, and when Christian theologians treat this problem as something that calls into question the existence of God, they are giving it more importance than it deserves (as a theological question). If this world is all that there is, then the problem of suffering is enhanced - for in the face of suffering and death, how can meaning be established? Yet if - as Christian theology insists - there is more to life than what we can perceive with our immediate material senses, then it is possible to assert that meaning (and therefore the language of faith - Godtalk - theology) persists in the face of suffering.
One way of bringing this out is to return to the question of Voltaire and the response to the earthquake in Lisbon. There was no immediate cessation of belief in God on the part of the residents of Lisbon, rather the opposite. It was only on the cultured sensibilities of Voltaire and his ilk that this event had such an impact; as Hart implies, it was only to theodicy - which, as a form of justifying God to humanity, cannot be orthodox Christianity - that such events were a shock. I do not believe it to be accidental that it is to the increasingly affluent and cultured despisers of faith that such traumas are experienced as shocking. Those who spend their lives more closely engaged with the daily reality and struggle for existence, who are much more acquainted with suffering on a daily basis, are also the ones in whom religious faith is most deeply rooted. (But then, they tend not to be educated in the Western sense, so their views don't count...)