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.
“A friend said to me, 'Be glad for your troubles - they strengthen you.' Well, if that's the truth, I'm going to be so strong they'll have to beat me to death!”