One common cause of argument between friends is that involving a member of the opposite sex. Perhaps, your friend has broken up with someone who, then, has shown interest in you. Since the friend has ended the relationship with this person, you do not feel disloyal by talking, going out, etc. with him/her. However, the friend finds your acts as an affront to your friendship.
In recording this in your diary, you may wish to follow the model of published diaries such as that of Anne Frank. You can also write the entry mostly as one writes dialogue in a literary narrative.
I would agree with the above post. Think of a time you have had a disagreement with a close friend and how you felt at that time. Your journal entry from your point of view should be an easy one. From your friends point of view may require more thought.
Write about a real event. Conjure up the last time you were actually mad about something. If that idea seems too personal, pick a time that this happened and you and the other person are clearly over it.
If it was a real situation, you know you'd have no trouble talking about it (and your feelings) to someone. So just do exactly that.
Pick a situation that may include school hours that makes your time for friends very short and so it's easy to describe the misunderstanding between them two. Ending with, where they meet up or call each other to clear the misunderstanding will enhance the ending with a bit of dram. Hope you found it helpfu.