Man is eager for vengeance and God is eager for forgiveness.
There is only one against whom we have all sinned and we keep sinning, and yet he is the only one whose posture of forgiveness is more eager than eager. He has grace like riches (Eph. 1:7, 2:7). He doesn't have to watch his spending. He forgives like it's going out of style.
A fellow sinner may forgive but it takes some working up to do. In some cases, he may even be eager to forgive but this eagerness does not come naturally. In many cases, though, there is not eagerness but dutiful obligation. We bring our sorrow, our repentance, our request for pardon, and we receive questions, probing, testing, measuring. We deserve this, there's no question about it. And really repentant persons will accept the difficulty of an offended party's forgiveness as part of that repentance. So we slink, tail between our legs, chastened and stung. It has to be this way because of the nature of human hurt and the antisocial nature of sin.
But, genuinely sorrowed over our offense, aren't we deep down hoping, craving, desperate for the offended not to stand off, arms crossed, waiting for us to drag ourselves into a posture of penitence, but smiling, ready to accept us again? And so our God runs to us. And he tells us to approach his throne with confidence (Heb. 4:16) to receive grace in our time of need.
The cross of Christ both proves and founds God's eagerness to forgive. Because of Christ's propitiating sacrifice, planned in love from eternity past and effectual to eternity future, we have no hoops to jump through, no qualifications to meet, no penitent mantras to intone, and no cowering to do. The act of God's forgiveness is not a muted, somber affair, but a "time of refreshing" (Acts 3:19-20).
His lovingkindness endures forever. He is not just quick to forgive, but eager and aggressive. Forgiveness is flowing out of him. Your heavenly Father is not a miser with grace. He is a fountain of forgiveness.
"Forgiveness is mainly that the love of the offended shall flow to the offender, notwithstanding the offense. It is love rising above the dam which we have flung across its course, and pouring into our hearts. Our own parental forgiveness is in some feeble way analogous to God's, and shows us that the essence of it is not the suspension of penalty, which may or may not be the case, but the unchecked and unembittered gift of God's love to the sinner."
—Alexander McLaren, "Christ's Claim to Forgive, and Its Attestation" [emphasis added]
God's forgiveness is like love rising over the dam, yes, a brimming overflow, but it's also like love rushing mightily through a dam break, flooding freely.