Almost as a prerequisite for this topic, before you can really have a good listener, you will need to explain why it's important to know more about Islamic teachings. Most people you come across will literally not have a clue why you would even be interested, or why they should be.
5. Confusing current events become understandable. Once you learn what's really going on, the scary terrorist events that make you think, "Why are they doing this?!" are suddenly illuminated, and you know exactly why they're doing it, and why most westerners don't have a clue about what's going on.
You would think that learning about Islamic jihad would make you hate Muslims, but strangely enough, it does the opposite. Most Muslims are in an even worse situation than the infidels. The more you learn about Islam, the more sympathy you have for Muslims who had no choice in the matter and cannot escape without risking their lives and the lives of everyone they love.
But sometimes learning about the subject is upsetting. It is a shock to learn what's in the Koran, knowing that one and a half billion human beings believe this is the final message from the supreme ruler of the universe.
But after you get over the shock, it makes world events less upsetting. You will understand what's going on for the first time. You will no longer feel as exasperated or wonder what the hell is happening in this crazy world. You'll finally understand.
Of all the benefits of learning about Islam, this is probably the one that had the most impact on me. Political events that have been happening since I can remember — the hostage situations and hijacked planes and bombings all seemed so unnecessary and confusing. And you can watch the news all day and get no clarity whatsoever about why these things are happening and what they all have to do with each other. It's a relief to finally comprehend the bigger picture.