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.
Above these universal themes 'Truth Will Set U Free' is also a song composed for those who were born gay. I am a straight man so I do not profess to understand or know what a LGBT person experiences but I do recognize injustice when I see it.