Romeo is very much like the play itself: full of paradoxes.
Just as Romeo and Juliet are never meant to be together, Romeo is never meant to feud with his enemies. When he does, tragedy ensues.
Shakespeare envisions Romeo as both a lover and a fighter, full of paradoxes, dualities, and oxymorons. In Act I, Romeo's first monologue is full of opposites:
O brawling love! O loving hate!
O any thing, of nothing first create!
O heavy lightness! serious vanity!
Mis-shapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire,
Still-waking sleep, that is not what it is!
This love feel I, that feel no love in this.
Dost thou not laugh?
Romeo is torn between fate and feud, two major themes and dualities. In Acts I and II, he believes his destiny is to love Juliet, no matter what her name is. Later, after Mercutio and Tybalt are killed and he is exiled, Romeo believes it is his fate to die by his own hand.
Notice that Romeo is never meant to fight the Capulets: he fights against the family curse the entire play, only to fall prey to it in an instant ("I am fortune's fool!") in Act III.