Are you a conflict avoider? I am! Surprised? True, I'm an attorney, divorce mediator and specialize in conflict resolution, but that's other people's conflict. To that, I say, Bring it On! I'll even step in uninvited to help resolve a brewing conflict. When the conflict involves me, that's an entirely different story. I'll go to great lengths to avoid conflict aristing and shy away from it once it has appeared.
The problem with avoiding conflict in your relationships is the same problem as avoiding any thing in your relationships that is uncomfortable but true. It doesn't go away. It doesn't diminish. It escalates. It simmers until it boils over. Something that started out as a minor scuff grows into a full blown problem.
Conflict avoiders usually settle into one of two camps - painfully passive or offensively aggressive: "Oh, don't worry, that's o.k. I'm sorry my body got in the way of your shopping cart." vs. "You idiot, how dare you bump into me. What the bleep is wrong with you!" Either way you are avoiding dealing with the conflict, or potential conflict, head on. You are coming from a lack of skills and thus lack confidence in your ability to resolve conflict in an assertive and constructive manner.
Being Assertive trumps being aggressive or passive just about every time. Assertiveness training gained popularity in the 1970s and it's back. A couple of the big books that started the movement are, When I Say No, I Feel Guilty by, W.J. Smith, and Pulling Your Own Strings by Wayne Dryer. And here is a great primer article on the topic from Mental Help.
To be assertive takes some self-awareness and lots of practice, if it isn't something that comes naturally to you. When you are assertive you are honoring your personal interests, desires and feelings without complete disregard for those of others. You are asking for what you want in a clear and direct manner while respecting the boundaries of all involved. You are not bulldozing nor are you subjugating your interests for another's. You are standing strong and being respectful in the process.