Excuses given are along the lines of "I never win an argument with you" and "you've studied it a lot more than I have, it's an unfair discussion".

This suggests that such discussions often take an adverserial tone. Have you tried to avoid this? I would say that if you want to convince someone, the absolutely first thing you should do is to make sure that they feel the discussion isn't about anyone winning or losing, but rather searching for the truth together.

Which is not to say that you couldn't convince people by winning an argument with them. Of course you can. But they're much more likely to actually become convinced if they feel like they had a role in coming up with the right answer, and you only helped them along.