When considering the question of evil, the easy part to explain is why there is pain, poverty and sickness, because if we truly understand the nature of our sinfulness, we realize that the world is much better than any of us deserve. Therefore, the real difficulty with the question of evil is understanding why some enjoy health and happiness in spite of the fallen nature of man. How does a just God endure the rampant corruption that goes on this world when it seems that justice would call for its immediate destruction? Hermann Bavinck answers as follows:
"Time and again Scripture refers to this mercy of God as it contrasts
with the attitudes of humans. His mercy is great, without end, tender
like that of a father, is shown to thousands, and after periods of
chastisement returns. In the New Testament, God, the father of
mercies, has revealed his mercy In Christ, who is a merciful high
priest and further shows the richness of his mercy and the salvation
of believers.
"The goodness of God, which spares those who are deserving of
punishment, is called forbearance or patience. Scripture frequently
mentions this attribute as well. It was made manifest throughout the
time before Christ and even now, in accordance with the example of
Christ, is still frequently displayed to sinners." (Reformed
Dogmatics, vol. 2, p. 213)
It's also important to understand that's everything that goes on in the world is under God's control. Nothing happens by chance, and many draw great comfort from knowing that all things are governed by His goodness. Charles Hodge speaks of God's providence as follows:
"As God is infinite in power and wisdom, He can control all events,
and therefore the course of events must be in accordance with his
will, because He can mould or direct that course at pleasure. It is,
therefore, evident, first, that events must be the interpretation of
his purposes, i.e., of what He intends shall happen; and secondly,
that no objection can bear against the purpose or decrees of God,
which does not bear equally against his providence." (Systematic Theology, vol. II, pg. 322)
The history of Joseph in the book of Genesis is a remarkable example of how God's goodness works through the sinful intentions of others. After Joseph had been sold into slavery by his brothers, he forgave them for their wrongdoing and explained to them that it had all been planned my God from the start, saying:
"And God sent me before you to preserve you a posterity in the earth,
and to save your lives by a great deliverance. So now it was not you
that sent me hither, but God: and he hath made me a father to Pharaoh,
and lord of all his house, and a ruler throughout all the land of
Egypt." (Genesis 45:7-8)
Speaking on passages such as this, John Calvin has the following to say:
"If I mistake not, I have already shown clearly how the same act at
once betrays the guilt of man, and manifests the righteousness of God.
Modest minds will always be satisfied with Augustine’s answer, 'Since
the Father delivered up the Son, Christ his own body, and Judas his
Master, how in such a case is God just, and man guilty, but just
because in the one act which they did, the reasons for which they did
it are different?'" (Institutes I, Ch. 18, Sec. 4)
Herman Bavinck comments that God's glory is made the most evident when it is displayed in such contrasting contexts:
"Certainly, it cannot be denied that we witness God's sovereignty at
its most brilliant when he a magnifies his wisdom in human folly, his
strength in human weakness, and his grace and righteousness in human
sin." (Reformed Dogmatics, vol. 2, p. 245)
Of course, for justice to truly be just, all accounts must eventually be settled. And though there may be an apparent imbalance as the corrupt sometimes prosper in life, eventually all of us shall stand before the throne of God to give a reckoning:
"[F]or we shall all stand before the judgment seat of Christ. For it
is written, As I live, saith the Lord, every knee shall bow to me, and
every tongue shall confess to God. So then every one of us shall give
account of himself to God." (Romans 14:10-12)
EDIT:
It has been objected that I begin with my argument with the presupposition of the fallen nature of man and his consequent sinfulness. This question is easily resolved by appealing to the divine authority of God's Word:
"For all have sinned, and come short of the glory of God;" (Romans
3:23)
Of course, there are those who reject the authority of the Holy Scriptures as well as the sinful nature of man. It might be said that this is really the heart of the issue because it's not just a rejection of the Bible's authority, it's also the rejection of the testimony of their own conscience:
"For when Gentiles who do not have the Law do instinctively the things
of the Law, these, not having the Law, are a law to themselves, in
that they show the work of the Law written in their hearts, their
conscience bearing witness and their thoughts alternately accusing or
else defending them, on the day when, according to my gospel, God will
judge the secrets of men through Christ Jesus." (Romans 2:14-16)
Man's sinfulness is the very obstacle preventing the just recognition of God's authority. For that reason, its recognition can be thought of as a prerequisite to any meaningful treatment of the subject. The traditional idea of theodicy generally begins with the assumption that there is evident injustice in the world for which God needs to be defended. It also usually assumes that man is in some way qualified to render a verdict with respect to God's justice. I deny both of these assumptions, especially because it's a travesty to suggest that the very people who refuse to recognize their own sinfulness may rise up and stand in judgment of God.
For those who would take such a position, there's nothing more to say. No evidence and no cleverly formed arguments can ever suffice to overcome the blindness that results from a hardened heart. Repentance is the only solution for that, pleading for God's mercy to grant the redemption that was purchased by the blood of Jesus Christ. For those who deny their own sinfulness, there remains no other recourse, and I refuse to enter into such a debate. As Bavinck so poignantly observed:
"[Scripture] does not put itself on a level below us to ask for our
approving or disapproving judgment on it but takes a position high
above us and insists that we should believe and obey. Scripture even
expressly states that the unspiritual cannot understand the things of
the Spirit, that they are folly to them, that they reject and deny
them in a spirit of hostility (1 Cor 2:14). The revelation of God in
Christ does not ask for the support or approval of human beings. It
posits and maintains itself in sublime majesty. Its authority is
normative as well as causative. It fights for its own victory. It
itself conquers human hearts and makes itself irresistible."
(Reformed Dogmatics, vol. 1, p. 505)