Why won't Romeo fight Tybalt? Support your answer with evidence from the text.

Romeo thinks he is part of Tybalt's family now that he has secretly been maried to Juliet, Besides, Romeo was never very much of a fighter, 

I do protest I never injured thee,
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.