First is that it seems to me that they make God responsible for evil. If the evil is allowed by God in order for a particular good to obtain, we must ask ourselves a couple questions. One would be, is the good that comes from the evil necessary to God’s plan? If it is, then the evil is also necessary which seems to me to lead directly to God planning evil. In fact, without the evil, a good necessary to the plan of God could not obtain. If we say that the good is not necessary to the plan of God, then we have the question still of why God allowed it. If it is the plan of God that the good obtain, we should ask is it possible for the good to obtain by some other means which does not require the evil. This would seem to lead to the conclusion that the evil is most arbitrary on God’s part. If the good is not necessary to the plan of God, then the greater-good explanation has lost is major premise.
A second problem is that of social justice. If God permits the evil to bring about a good (which is necessary to the plan of God), then how do we explain the commands in the Bible for believers to stand against evil. If the evil is stopped, then so is the good which means by obeying God we actually thwart the plan of God. For example, consider the matter of abortion. Since abortion is a reality and I would say an evil, we must conclude (under the reasoning of the greater-good) that God has allowed it for some good. If we stop the evil, we prevent the good. If one argues that the good is that Christians stand against the evil, what is the answer when Christians do not stand against the evil and it continues unabated? One can apply the same reasoning to slavery in the US.
A third would be how to determine how much good is necessary in order to justify the evil? How would that be measured and here I know of no cosmic scale that would serve such a purpose. It seems that it would follow that if good comes from evil the greater the evil the greater the good. Why should one not argue then that it is better to have a lot of evil than not have any evil, in fact, evil now results in good, so evil is good at least instrumentally. If good is measured in that fashion, good is relative. Something in all of this strikes me as being convoluted. It is similar to the argument of Romans 6 where Paul asks if we should sin that grace might abound. His answer is God forbid.
Fourth (there are other reasons I think the greater-good fails, but these four will be enough for now), the greater-good seems to place the Christian in the position of showing the good that obtained from the evil (an inductive approach). In fact, as I said earlier, that is what many are attempting to do which I find very unconvincing as a support for the greater-good theodicy. This is especially true with such evils as Stalin’s slaughter of upwards to 60 million people. If the good is always larger than the evil, then surely no one should have missed the good, but alas it is not so as we cannot point to any sizable good in that case. The greater-good denies that any evil/suffering is possibly gratuitous, that all evil/suffering has a purpose which is some greater good. If this is so, then we should be able to show the evidence that supports the claim. This I think cannot be done and hence undermines the greater-good explanation. Of course, I think if we could find a verse in the Bible that states this to be the case, then we should accept the greater-good. However, I am unconvinced that any such verse can be found. I want to be clear here, I am not saying that God never brings good out of evil, but that is entirely different from saying that that is the moral grounds on which he allowed the evil. Further, I would say that in those cases that God does so in spite of the evil, not because of the evil.