The wicked man writhes in pain all his days, through all the years that are laid up for the ruthless. Dreadful sounds are in his ears; in prosperity the destroyer will come upon him.
Eliphaz is not talking to Job as a friend or a counselor. He is attacking him as an accuser. Right off the bat he swings at Job, accusing him of not fearing God (Job 15:4). From there he launches into a theology that builds a case for a God Whose primary relationship with humanity in this world is to punish sin.
When Eliphaz sees God as the Punisher, it follows that all suffering is thus God's way of getting back at sinful people. When people are sinful, yet prosper, it is because they abused others. And eventually when a prosperous man loses it all, it is because God is judging a great sinner. The logic of Eliphaz's theology thus points an accusing finger at Job, charging him with being an abusive sinner whose evil led to his loss of everything.
But there are some major problems with Eliphaz. He makes for a great fundamentalist hellfire and brimstone preacher. But he does not have a right understanding of God. His observations about humanity are conveniently skewed as well. I kind of see him as the Fred Phelps of Job's generation. "God Hates Job!" would be his placard. And conveniently, his punishing principles would allow him to subscribe to a theology that creates multiple protest signs. His is a "God Hates (fill-in-the-blank)" way of understanding humanity and our responsibility before God.
Of course Eliphaz has it all wrong. Nothing works as rigidly as he sees it. Sinners can appear to prosper until their end. People die in luxury all the time. Wise and righteous people may suffer affliction. If the world was as Eliphaz imagined it, utopia would be ours, for only the righteous would have money, power, and influence. But the opposite is the general norm. Eliphaz's theology proves itself to be a delusional pipedream.
The fatal flaw that I see in it is a lack of eschatology. Eliphaz can only see reward and punishment in this life. And that leads him to assume his absurd stance on sin, punishment, and suffering. However, if God can punish people or reward people beyond this life... the whole perspective changes. And that is why a good doctrine of future things informs our understanding of sin, life, our present circumstances, and our duty before God.