Introverts and extroverts in conflict, a flammable recipe. Are you considering how introverted or extroverted people are when you're trying to resolve a conflict? Those two ends of the spectrum have very different needs, especially in a conflict.
Extroverts have a need to think out loud and speak immediately about what's on their mind. They use an assertive and integrative style and take conflicts head-on. Extroverts quickly regard introverts as distant and detached, silent and too slow to respond. They have the feeling they have to work really hard to get a response.
Introverts listen, think and weigh things to say in their minds. They are often less assertive, want to compete less and in general try to avoid conflicts. Introverts quickly view their extrovert counterparts as poor listeners that speak before thinking and try aggressively to make their point.
Side note: I understand the whole introvert/extrovert thing is not a dichotomy, but rather a spectrum. And that a lot of people are considered ambiverts. Also, how outgoing you are also depends on the context you're in: being with close friends or with a group of stranger matters a lot. So don't immediately put someone in the introvert or extrovert group, but assess each situation individually.
Here's a great tip (from The Introverted Leader): go on a walk together. Talking about an issue while walking not only leads to more creative ideas, it meets the needs of introverts and extroverts better than sitting across each other face-to-face. Extroverts can think out loud and ask questions without coming over as an attacking opponent. Introverts can listen and think without having to spend much energy on making eye contact and socially desired listening behaviors.