Disagreements happen. They're a fact of life. Each person has their own feelings and experiences, so it makes sense that not everyone will see eye to eye. In fact, different perspectives are what make life interesting and allow learning and growth. Problems arise when disagreements become arguments.
Arguments happen when disagreements are expressed in an "I'm right; you're wrong" sort of way. They are often born from and fed by difficult emotions – anger, sadness, hurt, helplessness, and confusion. These emotions tend to block the acknowledgement of the other person's perspective. The situation becomes "me" vs. "you," and everyone ends up frustrated.
Here are some steps to help you communicate:
Just the Facts: It's best to stick to the facts rather than bringing in feelings, or pretending you know more than you do.
For example, instead of saying to your friend, "You're mean. You didn't invite me to your party. I know it's because you're jealous of me," start with, "I wasn't invited to your birthday party."
That's it. You don't know why you weren't invited. Your friend hasn't told you. So you only know this one fact.
Validate: Next, validate the other person's feelings and perspective. Nobody likes to be accused of something, and people get way less defensive if you give them the benefit of the doubt.
Following the example above, you might say to your friend, "I know it's kind of awkward to talk about this," or "I'm sure you couldn't invite everyone in the class," or "I'm sure there's a reason."
Use "I" Statements: After giving the other person the benefit of the doubt, make sure to focus not on what they did or said but on how the facts of the situation affected you. Your friend may not have meant to hurt you, so don't accuse them of that; but you were hurt, and it's okay to acknowledge that.
So, instead of saying, "You really hurt me by not inviting me," stick with "I felt really hurt that I wasn't invited."
Compromise/Negotiate: Try to compromise; or if you can't, try to negotiate some other solution. If it is awkward to ask your friend to invite you in the future, ask if they can hang out with you some other time. If they don't seem interested, don't push the issue. You can always ask them to think about it, and follow up with them later.
The most important trip you may take in life is meeting people halfway.
Avoiding arguments doesn't mean that you can never express your disagreement with others. It just means that you have to communicate in a way that lets both sides talk. Use an approach that says "how can we resolve this situation?" or "help me understand." Even if you don't end up getting the answer you want, you will still feel heard; and that's a lot better than feeling frustrated and angry.