I'm a sociology major from UCSD, and from my experience, arguing about race, is like arguing about religion. Nobody convinces anybody, and it's a huge waste of time. The only way people really become convinced of racial inequality, is if they literally take some classes on it. Usually people who are extremely conservative will be very defensive to your opposing position, so he won't hear you out. But classes introduce the idea more neutrally, as opposed to these verbal debates that have a propaganda-esque vibe to it.