Biases make it extremely difficult to persuade someone with an opposing opinion. If it’s someone who respects you, you have a good chance. But even then, changing their mind likely won’t happen overnight.
Often what prevents two people from seeing eye to eye is individual blind spots. It’s rarely a case of one person being absolutely right and the other person being absolutely wrong.
And the weak spot in most arguments is often in what wasn’t said. Lots of facts might have been stated, but what ones weren’t mentioned?