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.
“When I was a boy I was told that anybody could become President; I'm beginning to believe it.”
“Most of the great directors I've worked with - De Palma, Spike Lee - like rehearsals.”