Each 'Eid is a Day of forgiveness.
When a Muslim assemble in the congregation of the Day, they all whole-heartedly pray for forgiveness and strength in faith. And Allah has assured those who approach Him with sincerity of His mercy and forgiveness. In that pure assembly and highly spiritual congregation any true Muslim would feel ashamed of himself before Allah to hold any enmity or ill feelings toward his brethren.
A true Muslim would be deeply impressed by this brotherly and spiritual assembly, and would overcome hid feting if he has been exposed to any. Consequently, he would find himself moving along with others responding to the spirit of the Day to purify his heart and soul.
In any case, he would forgive those who might have wronged him; because he himself would be praying for Allah's forgiveness, and would do his best to acquire it.
The spirit of this highly devotional assembly would teach him that if he forgives he will be forgiven.
And when he forgives, the virtue of forgiveness will be mercifully exercised by Allah, and widely exchanged between the Muslims. And that marks the Day as a Day of Forgiveness.