The argument from evil is usually cast in terms of an allegedly inconsistent tetrad:
i) God is omnipotent
ii) God is omniscient
iii) God is benevolent
iv) Evil exists
One solution is to deny a horn of the proposed dilemma. Some freewill theists tweak (i) by stressing God's self-imposed limitations. But there's not much milage to be had in tweaking (i). Even if God doesn't exercise his omnipotence, he's capable of stopping or preventing evil. Moreover, even if one denies (i), that hardly refutes the argument. As John Piper noted, in response to Rabbi Kushner:
God does not need to be “all-powerful” to keep people from being hurt in the collapse of a bridge. He doesn’t even need to be as powerful as a man. He only needs to show up and use a little bit of his power (say, on the level of Spiderman, or Jason Bourne)—he did create the universe, the Rabbi concedes—and (for example) cause some tremor a half-hour early to cause the workers to leave the bridge, and the traffic to be halted. This intervention would be something less spectacular than a world-wide flood, or a burning bush, or plague of frogs, or a divided Red Sea, or manna in the wilderness, or the walls of a city falling down—just a little tremor to get everybody off the bridge before it fell.
Roger Olson was outraged by Piper's response, but he didn't attempt to directly rebut Piper's observation, which is irrefutable.
Some freewill theists deny or minimize (ii). But that's unsuccessful. Even if (ex hypothesi) God doesn't know the future, a moral agent needn't be 100% certain about a ripening outcome to see what's highly likely to transpire unless he intervenes. Suppose a mother loses control of her baby stroller, which goes careening down the hill, heading straight into a busy intersection. A pedestrian halfway up the hill is in a position to intercept the stroller just in time. All he has to do to ensure a tragic outcome is to do nothing. Inaction, in combination with gravity, terrain, wheels, &c., guarantees the outcome.
The hypothetical pedestrian didn't create the situation. Didn't cause the mother to lose control. Didn't put the baby in danger. He's far less responsible than the God of freewill theism (be it Molinism, open theism, or simple foreknowledge Arminianism). Yet the pedestrian's nonintervention is culpable.
Or suppose the tragic outcome isn't a dead certainty if he fails to intercept the stroller. Suppose there's only a 40% chance the baby will die in a collision. But even so, we'd consider the pedestrian to be blameworthy.
Or a Christian could challenge how the atheist defines (iii). What if God is not benevolent in the way we wish or hope? Isn't Yahweh pretty hard-nosed? And the harsh events we read about in Bible history are no different in kind than the harsh events we read about in the newspaper or secular history books. So why not adjust your view of God's goodness to the Bible and reality?
Finally, a person can deny (iv). And that isn't just hypothetical. Take Mary Baker Eddy or John McTaggart–as well as strands of Hindu and Buddhist philosophy that say the sensible world is Maya (illusory or delusive).
Freewill theists tend to operate with a priori notions of what God must be like. This comes out clearly when attacking Calvinism. So they may appeal to perfect being theology (as they construe it) to preemptively discount Reformed theism.
On a related note, John Wesley famously said that whatever the Bible means, it can't be that!–in reference to Calvinism (specifically, reprobation). Roger Olson takes the position that Reformed theism can't be true because it would make God untrustworthy.
Some freewill theists (e.g. Randal Rauser) take the next step by denying that God did some of the things attributed to him in the Bible, viz. "abhorrent" commands, like the command to sacrifice Isaac or the command to execute the Canaanites. Once again, this conflicts with their preconception of God's goodness.
The pattern here is to begin with a preconceived notion of what kind of evil is permissible in a world made by a benevolent God. But the dilemma for the freewill theist is that given the existence of horrific evil, that limits their explanatory options.
Considering their scruples, if evil didn't exist, it's hard to envision their conceding that a benevolent God would allow such evil to exist. If evil didn't exist, don't you imagine they'd rail against a philosophical theologian who proposed the possibility of God making a world in which atrocities like the Holocaust, child murder, &c., happen? Wouldn't they accuse the philosophical theologian of blasphemy for even entertaining that impious speculation?
But the existence of evil forces their hand. So they struggle, because it stands in deep-seated tension with their moral intuitions regarding what ought to be the case, given their expectations regarding what a benevolent God should disallow. If they had their druthers, if they were coming to this issue from scratch, in a world devoid of evil, certain evils would be incompatible with the only kind of God that can exist–from their viewpoint. As it is, they are stymied by the horrific and apparently gratuitous evils in the real world. And it makes they resort to hairsplitting distinctions when attacking Calvinism while exempting their own position.
Considering the way in which many freewill theists lay down a priori strictures regarding what a benevolent God would or wouldn't do, it would be more consistent for them to go whole hog with thinkers who say evil is illusory. That really does let God off the hook.
In fact, idealism is making something of a comeback in Christian philosophical circles. For instance, Robert Adams, "Idealism Vindicated," Peter van Inwagen & Dean Zimmerman, eds. Persons: Human and Divine. (Oxford, (2007), 35-54; J. Farris, S. Hamilton, & J. Spiegel, eds. Idealism and Christian Theology: Idealism and Christianity • Volume 1 (Bloomsbury, 2016); S. Cowan &. J. Spiegel, eds. Idealism and Christian Philosophy: Idealism and Christianity • Volume 2 (Bloomsbury, 2016).
Mind you, I find that wholly implausible. But given their theological priorities and moral presuppositions, if they were really serious, the most consistent theodicy for freewill theism is to reclassify evil as a massive illusion. That way they don't have to squirm over God allowing horrors which would be culpable for a human agent in his position.