What makes debate between Calvinists and their opponents so difficult is that it really boils down to a difference of basic hermeneutical principle. What makes Calvinism difficult for many to accept is the fact that they see the Bible pointing in the direction of a hermeneutical center, and that center is love. When the I John 4:8 says God is love, for agapocentrists, this isn't just a statement that God is loving, (except, of course, when he's unconditionally reprobating people), it is rather, that this is an essential characteristic of God that provides the fundamental motivation behind everything.
Consider Wesley's response to a biblical case for predestination in "Free Grace."
Whatever that Scripture proves, it never proved this; whatever its true meaning be. This cannot be its true meaning. Do you ask, "What is its true meaning then?" If I say, " I know not," you have gained nothing; for there are many scriptures the true sense whereof neither you nor I shall know till death is swallowed up in victory. But this I know, better it were to say it had no sense, than to say it had such a sense as this. It cannot mean, whatever it mean besides, that the God of truth is a liar. Let it mean what it will, it cannot mean that the Judge of all the world is unjust. No scripture can mean that God is not love, or that his mercy is not over all his works; that is, whatever it prove beside, no scripture can prove predestination.
What Wesley is saying here is that for him, God love is the central to his understanding of Scripture, and that, as he sees it, it ought not to be interpreted in a way that conflicts with its most fundamental theme.
With respect to the Law, Jesus seems to set love up as the hermeneutical center: love God and your neighbor and in so doing you will fulfill, at least in spirit, the whole of the Law. Paul, with respect to what came to be known as the Three Holy Virtues, faith, hope and love, put love as the greatest. With respect to any question on limits on the scope of love (Who is my neighbor?) Jesus, through the parable of the Good Samaritan, undercut the conception of "in group" versus "out group" which, to a regrettable extent, infects all human efforts to love others.
Calvinists say that, yes, God is loving, God saved people he didn't have to save, but besides loving, he has other fish for fry, other attributes to manifest. In particular God's glory would be diminished if he only manifested the attribute of loving in his treatment of us, instead of also creating persons destined to be unrepentant sinners on whom he manifests his wrath.
I had complained against Calvinism that it leaves an unacceptable gap between what God wants us to do and what God himself does. Of course, Steve and Peter have both pointed out that there are plenty of situations in which, depending on who you are, what is right for you to do is different from what it is right for someone else to do. But I was not talking about specific actions, I was talking about the traits of character that God manifests and the God expects humans to manifest. John tells us those who don't love don't know God because that is who God is. He doesn't say "those who aren't wrathful don't know God, because God is wrath." It is no doubt true that an infinite God has the right to exercise "tough love" in ways that would be unacceptable if humans were to behave in the same way towards others. We are not talking about "sloppy agape" here at all. Sin has to be repented of, actions and thoughts have to be repudiated, and that's got to be painful. But in agapocentric theology there is a symmetry between the character God commands us to have and God's character. God is more powerful and wiser than ourselves, but his fundamental purposes are the same as those we are told to develop within ourselves. If Calvinism is true, then God has certain traits of character which are good for him to have but not for us to have. To me, that leaves us, not with an Omnipotent Fiend perhaps, but certainly with a God with a divided character that seems to me schizophrenic.
The essay I have linked to is by Thomas Talbott, who is an agapocentrist who is also a universalist. Other agapocentrists are Arminians; they believe in God's loving purpose, but think that in order to have genuine love there has to be freedom, and that some persons will permanently choose not to accept God's love, and will, as C. S. Lewis says, lock the doors of hell from the inside. However, the character of God is the same for universalists as for Arminians. Calvinists, however, see God's character differently.
One further objection might be that it is wrong to have a "hermeneutical center," because if we have one we will screen out important biblical data that conflicts with that center. What one must do is take the Bible as it comes, with each part of it being regarded as no more fundamental than any part.
But doesn't everyone have a hermeneutical center? Doesn't everyone read passages that are harder to understand from the point of view of their hermeneutical center through passages that express that center? If someone says "No. We do pure exegesis here. We read the Bible in an neutral unprejudiced way. That's how we came to accept he doctrines of grace," my response is that I simply don't believe you.
Can there be shifts in hermenutical centers? Yes, but they are massive shifts in understanding that involve massive biblical evidence.
Does agapocentrism make the problem of evil more difficult? There is a sense in which it does. Persons who advance the argument from evil expect God's goodness to involve loving all persons, which agapocentrists agree with. They also have a tendency to equate love for us with a pursuit of our own temporal happiness, which agapocentrists need not accept. Calvinists can say that it just isn't morally necessary for God to behave lovingly toward every person, and there is a sense in which they can deflect or dissolve the problem of evil more easily than can agapocentrists.