Different Christians have different (valid) answers to the 'problem of pain' or human suffering, or evil - and each sincere and knowledgeable answer captures or highlights something of the truth; but not all of it - since that is the nature of answers.
(After all, how could anybody capture the whole truth in just one short sentence? The idea is absurd. And having written or uttered a sentence, how would be be sure that everybody understood it correctly?)
And there does not need to be one single cause of evil and suffering in the world.
There is the free will of men; the purposive Good-destructive evil of Satan and his minions (which themselves need explaining); the limitations - some logical and practical, other perhaps fundamental - on God's power and influence; the indifference (or hostility) of the 'non-living' world (e.g. natural disasters). And so on.
But at the bottom of it all is the fact, that ought to be blindingly obvious to anyone who understands enough about Christianity to become one, that nobody who knew anything about Christianity ever claimed that Christianity was about producing perfect or even optimal happiness in this mortal life on earth.
Surely it is crystal clear? (even to an Archbishop) that Christianity is about our happiness in the eternity after death and resurrection?
(Our happiness is this world is indeed affected by Christianity - very much so. But the degree to which perfect happiness is created - measured, as it will be, by existant, labile, partly corrupt evaluations - is not a measure of the validity of Christianity; nor is the failure of Christian belief to create perfect earthly happiness a refutation of its validity!)
This world and our mortal life is extremely important - and it is not merely 'a means to an end' - but surely the voices of the New Testament are unamimous and unambiguous that the Christian importance of mortal life is not about God making mortal earthly life maximally happy and eliminating pain and suffering on condition of belief...
Where (on earth) did people get that idea? Not from the Bible! That idea just is not a part of the message.
The provenance of the made-up notion that Christainity, if it were valid, would eliminate pain and suffering from the world is surely demonic, not divine.
This idea of suffering being a threat to the validity of Christianity is a pseudo-problem, falsely framed.
Which is why, having accepted this frame, the question cannot ever satisfactorily be disposed-of - 'doubts' induced by the sufferings of mortal life lead, not to answers, but to to more-doubts - and to the erosion of faith.
Which is not an accident.
We do indeed often seek an explanation of pain and suffering - and we may or may not find it (the reason is likely being personal to the seeker and specific to the cause - typically, general reasons will not satisfy us) - however our failure to understand the reason or meaning or causes for specific sufferings has nothing to do with the truth of Christianity (it is 'orthogonal') - this just is not a reason for 'doubts'.
The valid domain of consideration that may (sometimes, for some people) be induced by the existence of extreme pain and suffering and evil in this mortal life, is an enquiry concerning the relationship between God's Goodness and His Power.
Christians have been told unambiguously that God is wholly Good; also that he is the creator and the most powerful of 'god's. To understand evil and suffering some people need a satisfying general explanation of how these divine attributes might fit-together.
And any explanation must start either with God's Goodness, or with his power. Which divine attribute you start-with (and this is a metaphysical assumption that probably should be based on interpretation of divine revelation) determines the range of possible answers you will end-up-with.
But none of this is to do with the validity of Christianity supposedly being challenged by the existence of suffering and evil. Our ancestors knew this - and their direct experience of suffering was, on average, far greater than our own.
However, our own experience of evil is greater than theirs. They knew, with considerable precision, what was Good. Yet we live in a world of moral inversion in the official arena of public discourse, a world of evil routinely and by high status persons propagandized as Good; and of Goodness depicted as evil - all this by communications (including everything from the arts and sciences to advertizing and public relations) whose reach and influence is (via the mass media) now almost all-pervading and universal.
And THAT fact of living inside an actively-evil world, is the reason why modern people have been duped into supposing it is valid to state that the sufferings of mortal life constitute as lethal challenge to Christianity.
The debate is itself a product of modern moral inversion.
Note: Thans to commenter Joel whose questioning provoked this very full response: I hope it satsifies him!