What convinces is conviction. Believe in the argument you're advancing. If you don't you're as good as dead. The other person will sense that something isn't there, and no chain of reasoning, no matter how logical or elegant or brilliant, will win your case for you.
“I'm the one who has to look in the mirror, and after a while it begins to eat at you.”
“I mean, I've been in a hundred and fifty films; I don't want to just sit around and talk about things.”