A theologist like Leibniz is concerned with dogmas, which are like axioms: They are assumed to be true and form the basis of a logical system, that is supposed to consistent.

Beside that Leibniz contributes to a thousands of years old discussion about theodicy, the righteousness of god.

Let's look at the historical context first, because your bible verse is fitting:

In many cultures of the ancient world, misfortunes and disasters are said to be the result of a divine punishment. This can be seen in the old testament on many occasions, but it's basically the same in Greek societies etc. Christian scholars read the book of Ijob as an instance, where this thought is challenged: Ijob is living a righteous live, why is he punished?

The book itself doesn't really give an answer to that, but in the ancient world view kin liability applies. So even when Ijob was sinless, he inherits the sin of his forefathers, going all the way back to Adam.

Your bible verse (Romans 5:12) is referring to that, but if you read a bit further, this world view of the old testament is contrasted with the new testament. To paraphrase: Where one man (Adam) brought sin into the life of many, now one man (Jesus) takes the sin from all.

So in the Christian doctrine the argument, that bad things happen to us due to inherited sin doesn't apply anymore.

Which leads us to the scholarly discussion, which Leibniz is part of. The central dogmas (axioms) of Christianity relevant for the theodicy question are the following:

* There is only one god

* God is almighty

* God is all-loving

* God is understandable, since God revealed himself through Jesus.

The job of philosopher/theologist is to resolve, the perceived contradiction, that bad things are happening to good people and a loving, almighty God wouldn't allow that.

The most common solution is to drop one of the axioms, e.g. "God wants to help us, but he can't" (not almighty) or "God works in mysterious ways" (not understandable).

Leibniz instead doesn't sidestep the problem and argues, that even the best possible world can't be free from sorrow. I, personally, really like his line of thought, but this comment is already to long to describe it further.

I can't speak to Leibniz since I haven't studied his philosophy at all, but there seems to be at least a distinction between a fallen world (or a corrupted world) and a fallen man.

That is, you could take the view of some (so called) gnostic sects that see the world as a corrupted mess created by a demiurge. In such a view one could understand man as a divine spark that is imprisoned within this world, perhaps even maliciously tricked by that demiurge, and gnosis is the realization and means to escape. That is a kind of heresy that was argued against quite vehemently by the early church fathers (as well as Neo-Platonists like Plotinus for what it is worth).

That would be opposed to a view that the world is a good creation (or at least as good as was possible given the material available, in the vein of Plato's Timaeus) and man is the ambiguous thing, given free will and the choice to align itself with God. In that case, the fall of man is better seen as a rejection of a good that has been offered.