One way to look at your situation is that your having fights (i.e both of you are verbally aggressive, look for ways to minimize the other's feeling, don't speak to each other afterwards). Since you made the request, your partner may view these interactions as heated discussions.

There's a few things I'd have both of you do real soon. First, set up a time with no distractions in your apartment/house (phones, tv., computer and stereo off, give yourselves plenty of time and promise that neither of you will walk away when it's the others turn to talk).

Set up some mutually agreeable "rules" before you start: no interruptions or talking over the other; no accusations; each of you have to use a realistic amount of time when you speak (i.e  5-15 minutes); when one of you has finished,  the other summarizes what was said before the other begins. When the other has his/her chance to speak (same amount of time), the first person summarizes what was said before (s)he comments - and you trade off with this discussion. There can be more rules, but they have to be mutually agreed upon and focus on learning from each other.

Here's the hard part. Rarely are fights about "(s)he doesn't listen to me" or "(s)he tries to tell me everything I need to do". Usually, it's about two things - the "lens" you use to view life. The "lens" you use is a collection of your life experience and how you interpret people's actions and words. If you're an adult who is an only child and your partner came from a family of 12 brothers and sisters chances are you both approach shared and private time very differently. And neither approach is wrong. What is wrong is when you expect the other to know your thought process. Because you rarely know it yourself. Think about times you couldn't think of an answer to a tough personal problem. if you went into the the problem in detail with a friend, you might have come up with the answer - but it didn't happen until you verbalized the problem and your thought process.  

The second thing most fights are about is because the "platinum rule" was ignored. "The golden" rule is treat people how you want to be treated. The "platinum rule" is treat people how they want to be treated. If a person likes to have verbal fights and you don't and both of you want to stay together then the two of you need to mutually come up with ways that you can communicate the way you want that is acceptable to the other.

One last thing I'll write - conflict is part of any relationship - family, love, work and friendship. Things get worse before they get better when you work through a conflict because of the emotions involved. And conflict is dynamic - it never completely goes away. You and your partner might have fewer and fewer fights as time goes on, but you'll always have conflicting ideas about certain things. That's o.k. - it's normal.