Time magazine asks an excellent question, don’t you think? I do. The only answer I am muster to give is: because it is the right thing to do AND our Savior forgave his killers. Therefore, we ought to do the same.
BUT, if you are ashamed to forgive and to receive forgiveness, you must be convinced that Jesus Christ is blowing smoke or not real. The 4th century Persian bishop, Aphrahat said as much in his treatise On Penitents where he taught that a Christian in the state of sin should seek sacramental forgiveness as the Church taught. Aphrahat decapitates the sin of presumption and pride when he says,
… the man wounded by Satan should not be ashamed to confess his, and leave it behind, and beg for the medicine of penance. For gangrene comes if a man is ashamed to show his wound, and then the whole is harmed. Whoever is not ashamed has his wound healed, and goes back to battle again; but if gangrene comes, he cannot be healed, and he cannot take up his arms again.
So, why forgive? Because if one doesn’t forgive the sins of another, how will you face your own humanity and the Savior face-to-face?
Aphrahat, On Penitents 2-3 (Demonstrations 7), adapted translation by Frank H. Hallock, Journal of the Society of Oriental Research 16 (1932), pp. 43-56.