The unconditional forgiveness demanded of a Christian derives from the love of enemies demanded of a Christian.
When Christ said, "Love your enemies," what He actually meant was, "Love your enemies." That sounds obvious, but I suspect a lot of people take Him to mean, "Love everyone, including your enemies."
But although this is what Christ commands of us, it's not really what, "Love your enemies" means. An enemy isn't someone who happens to be included among the people you are to love. An enemy is one who hates you, who wills evil for you, who acts so that bad things happen to you and good things don't happen to you.
I know I tend to water down the idea of "enemy" when I see the word used in Scripture. As far as I know, I don't spend a lot of time with people who hate me, and though there are plenty of people who might be pleased if something bad happens to me, I doubt there are many who are actively working to cause me evil. (Me personally, I mean, as opposed to me as an American or Christian or whatever.)
So I do a lot of the "love the people who cut you off on the road" kind of substitutions. "Pray for those who drone on in meetings you attend." These are fine sentiments, but clearly they fall far short of Jesus' call to Christian perfection.
Love the person who wants you dead. Love the person who wants your children dead and your house burned down, who wants you sitting on an ash heap amidst desolation, weeping like Job. This is the love of enemies which gives birth to Christian forgiveness.
Such a forgiveness is not a philosophical position. We don't arrive at it by reason. The only sound argument for it is, "Jesus told us to."
That's not to say unconditional forgiveness isn't reasonable, or that we can't identify its good effects. But we don't forgive unconditionally because it's good for us both spiritually and psychologically, we do it because Jesus commands us to.
It's a tricky point, since by the fact Jesus commands us to do it we know it is good for us, and the fact that it's good for us is [at least one of the reasons] why Jesus commands us to do it. But if we reason our way to unconditional forgiveness, if the premise upon which we accept it is not, fundamentally, "Jesus commands it," then there is the very real possibility that circumstances might arise in which we find that the natural reasons for which we forgive unconditionally are no longer valid. If I forgive others because of the psychological benefits letting go of a grudge gives me, then if there comes a time when I decide the psychological cost of forgiveness outweighs the psychological benefit, it would be irrational for me to forgive.