I am not sure who told you otherwise but dueling comes in many shapes and forms. The only rule that always remains is that it is one on one. Of course dueling with one sword in one hand is the most courteous. 

1st Style: You gain a +2 bonus to damage rolls with all melee weapons.

2nd Style: When rolling initiative, you can designate a target for combat. You gain advantage on all melee attacks against that creature and you can not be disadvantaged when making attacks against that creature. If the target drops to 0 hit points, you can mark a new creature as a free action.