Why won't Romeo fight with Tybalt in Romeo and Juliet?
Since he is now married to Juliet, he doesn't want to fight with her family, for Tybalt is her cousin.
"Tybalt, the reason that I have to love thee
Doth much excuse the appertaining rage
To such a greeting. Villain am I none.
Therefore, farewell. I see thou know’st me not." 3.1
Although Romeo is rather vague in his explanation (because he may be trying to keep his marriage to Juliet a secret because of the feud) , Romeo says that he loves him and refuses to fight him for presumably that reason: Juliet.
He goes on to say: "But love thee better than thou canst devise,
Till thou shalt know the reason of my love.
And so, good Capulet—which name I tender
As dearly as my own—be satisfied." Which also goes along with that.
Not to mention, it is forbidden in the streets to fight, which is what the Prince of Verona says at the beginning of the play. Romeo is also trying to keep everyone from getting in huge legal trouble.