Even when you think you're standing up for yourself and presenting your ideas in a fair way, your friend is likely to perceive you as being overly aggressive, because you're on opposite sides of the fence when it comes to the way you express yourselves, especially in an argument. Your buddy may fall back on logic and quantitative proof to make their point, while you'll be more into going with your gut reaction and doing whatever it takes to make yourself heard. This could result in raised voices, saying things you regret later and more.
A large part of the problem here, of course, is that you'll both be projecting things onto the other. When you catch yourself tossing accusations their way, stop and assess your own behavior. It may be that you're really talking about yourself. It will take a lot of patience to build this friendship, but it is possible.