What argument does friar Lawrence used to prevent Romeo from killing himself?

You are no doubt alluding to Act III Scene 3, in which the Friar says to Romeo, "Hold thy desperate hand" and later in the same speech "Wilt thou slay thyself?" From this a number of editors have inferred that Romeo must have attempted to commit suicide immediately before the Friar says this, which does make sense of the Friar's speech. However, Romeo does not say that he is going to kill himself, but rather, "Tell me in what vile part of this anatomy doth my name lodge? Tell me, that I may sack the hateful mansion." In this rhetorical speech, he offers to rid his body of whatever part contains his name. It's rhetoric, and he doesn't mean it, because he knows names don't work like that. But perhaps he is waving around a knife, and the Friar gets the impression that he is planning to use it to kill himself, and proceeds on that assumption. Anyway, the friar has been offering the same advice since before the Nurse showed up: "Count your blessings." He becomes more vehement at this point, possibly because he thinks Romeo is actually going to hurt himself, but the message has not changed.