In Romeo and Juliet by Shakespeare, how does Romeo show that he is not brave?

After Romeo has slain Tybalt and been sentenced to exile by the Prince, he takes refuge at the cell of Friar Lawrence and learns his fate from him.  When Romeo learns that he's been banished, he becomes desperate, and when he hears from Juliet's nurse of how much Juliet cries over what has happened, he completely loses courage.  He draws his dagger as if to end his own life with it, until the Friar compels him to "Hold [his] desperate hand!" asking, "Art thou a man?" (3.3.118, 119).  Such a question indicates that the Friar believes Romeo to be behaving without mettle, without bravery.  He chastises Romeo for this, saying that Romeo's behavior and complaints "[Digress] from the valor of a man" (3.3.137).  In other words, his wailing and histrionics swerve away from the the courageous behavior the Friar would normally expect from a man.  Romeo seems not to consider or care that his suicide would likely kill Juliet, or cause her to kill herself as well.  He behaves with cowardice and a lack of gratefulness that a punishment that should have been death was changed to exile only.