To understand what Christian forgiveness is, you need to understand the "forgiveness" part as well as the "Christian" part.
Objectively, forgiveness involves matters of justice, the giving to someone what is due him.
If we enter into a pig buyer/pig seller relationship, then what is due me is the pig and what is due you is money in the agreed upon amount. (Of course, the agreed upon amount is not necessarily just, but that's another question.) If we enter into a pig stealer/pig owner relationship, then what is due me is punishment for the harm my theft has caused and what is due you is the pig I stole (plus, perhaps, some further reparation).
In these terms, forgiveness means a person who in justice is due some good cancels the debt. The Latin verb used in the Lord's Prayer ("forgive us our trespasses as we forgive those who trespass against us") is dimittere, which can mean to renounce or give up and is the root for the English word dismiss. If I steal your pig and you forgive me, you are renouncing your claim to reparation (and, if you're a Desert Father, even your claim to the pig).
Suppose someone is in a bad mood and snaps at you when you try to talk to them. Later, they come to you and apologize for their harshness, and you say, "That's all right, I forgive you."* What exactly are you forgiving? In other words, to what are you renouncing your claim?
I think what's renounced in such cases is very often the right to act on feelings of hurt, offense, or resentment. Since this is a right people do claim for themselves, renouncing it does seem like an act of forgiveness, and many Christians do believe they are following Christ's commandment to forgive when they renounce it.
But if you accept what I've written so far, an act can only be forgiveness if it renounces something that is due in justice. Do we have a just claim to the right to act on hurt or offended feelings? Are we truly due that right?
I don't think we are. I think we are due an apology; the harsh words have unjustly caused an injury, and the person who causes an injury owes some comfort or care to the person injured.
But if this is the case, then properly speaking unconditional forgiveness is the only forgiveness we can offer. If we wait to forgive until the person has apologized, then we've already received what is due us. In fact, what we call our forgiveness is itself due the other person, as acknowledgement that their debt has been paid. "I forgive you," in this case, isn't a statement of forgiveness, it's a receipt for an apology. To refuse to accept the apology would be unjust.
All this suggests that the common social understanding of forgiveness needs correction, purely from the consideration of the object of the act. When you bring in the intention of the act -- the "Christian" part of "Christian forgiveness" -- then you're really talking about something scandalous.
* This assumes you're in a relationship in which the words, "I forgive you," can be spoken. There's probably something to be gained by thinking about who could and could not say those words to you in a sincere and unironic way without offending you.