In the Elizabethan time period, it was thought that a man too much in love is not actually a man at all, he is "effeminate". In this scene, Romeo fights with his two selves - the more manly version that Mercutio knows who would fight at the drop of a hat and the softer version that Juliet knows who tries to keep the peace as he does not wish to fight with his new wife's kinsman.
There is a lot of debate on this subject, but it can be argued that Mercutio (his name means a mercurial nature) fights Tybalt on Romeo's behalf both to restore Romeo's manliness and because Tybalt essentially calls him bi or gay and says he's in love with Romeo. It can be argued that this makes Mercutio especially angry because it's true. The dramatic irony there would be that Mercutio fights Tybalt so Romeo doesn't look effeminate, but it is actually (according to Elizabethan sensibilities) Mercutio who is effeminate.