Lest anyone be confused, let's give the last word on this one to Leo XIII:
The generally held argument that this sort of struggle washes away, as it were, the stains that calumny or insult has brought upon the honor of citizens surely can deceive no one but a madman. ... It is, to be sure, the desire of revenge that impels passionate and arrogant men to seek satisfaction. God commands all men to love each other in brotherly love and forbids them to ever violate anyone; he condemns revenge as a deadly sin and reserves to himself the right of expiation. If people could restrain their passion and submit to God, they would easily abandon the monstrous custom of dueling.
--Pastoralis Officii, September 12, 1891