Two of the attributes I've heard attributed to God are Justice and Mercy. These are often held in conjunction with the claim that God is perfect, so all of the attributes he possesses, he holds in perfection: so God is perfectly just, and perfectly merciful.
Now am I incorrect in thinking that there's a contradiction here? How can God be perfectly just and perfectly merciful? Here are what seem to me to be obvious definitions of justice and mercy:
Justice: getting what one deserves (whether positive or negative, i.e. punishment or reward)
Mercy: not getting what one deserves (usually purely in a negative sense, i.e. being spared the punishment one deserves)
Note that I've left open what it means to "deserve" a punishment or reward, and who decides this and what criteria they should use to judge. There are many different ideas and arguments here, but they don't affect the point I'm making, as justice and mercy come into effect after this decision has been made, however it is decided.
Now following on from these definitions, what does it mean to be perfectly just or merciful? Well these qualities only have meaning when they're applied to one person concerning their treatment of another. So for God to be perfectly just in regard to humanity, it must follow that everyone will get what they deserve. Likewise, for God to be perfectly merciful, it follows that no-one will get what they deserve, in terms of punishment. It seems to me obvious that should one single person not receive the punishment they deserve, perfect justice has not been observed. Likewise with perfect mercy, should one single person receive the punishment they deserve.
And there we have the contradiction: God cannot be perfectly just and perfectly merciful. For if he were to be perfectly just, according to evangelical theology, everyone would go to Hell. Conversely, if he were perfectly merciful, no-one would go to Hell. Now this contradiction cannot be brushed aside in a claim that in some mysterious way both are true, because we are talking about the fate of real human beings. A single person cannot both be in Hell and not in Hell (and no arguments here for quantum superposition please!).
How can we resolve this dilemma? Well there are two avenues open to us. One is to drop the idea that God is perfectly just and merciful; the other is to discard the doctrine that human beings deserve eternal punishment. The second avenue is the one I would recommend, but I think it is one evangelicals would be reluctant to go down, for obvious reasons. That leaves us with the first option, and I really don't see what would be hard about dropping this. After all, it's a core belief of evangelicalism that most people will receive some sort of punishment after death, but some will be forgiven. So why not just say that God is more just than he is merciful, in proportion to the number of people who are not forgiven as opposed to being forgiven? And leave it at that?
As an aside, evangelicals will resort to another doctrine to attempt to resolve this contradiction: substitutionary atonement. God must be perfectly just and perfectly merciful, but this puts him in a dilemma, which he solves by punishing himself (i.e. Jesus, who is the Son of God, who is actually God) for the sins of humanity. Now this is an ingenious idea, but is simply a sleight of hand, as it distracts one from the central contradiction. Aside from the question of whether it is just to punish someone else, or even oneself, for the crimes of another, the issue is simply not resolved. For justice and mercy are qualities which are shown to a particular person. So if we take the example of a repentant sinner, who has accepted Christ's sacrifice for his sins (whatever that may mean), has justice or mercy been shown to this person? Obviously, he has been spared his punishment, so mercy has been shown to him. Justice has not been shown to him, as he has not recieved what he deserved. So God has not been both perfectly just and perfectly merciful in his case, and so in the case of every person punished or forgiven by God. So this doctrine resolves nothing.