There’s no question that children have to learn how to relate to their peers (through 'thick and thin') as part of growing up. That’s part of what school is all about, and the staff who work in a school help the children to do that.
There is a clear difference, though, between a child who is being systematically bullied, and a child who is falling out with friends due to natural personality clashes or imbalances of power within friendship groups. This can happen especially when children with strong characters are involved.
Children are constantly learning how to be 'grown-ups', and there is often some dramatic element to a fall-out which children with strong personalities actually enjoy at the time, regardless of the consequences, because it attracts attention. It is only after the fall-out that the consequences are realised, and then they get upset.
On drilling down to the reason behind the fall-out, it can be the tiniest thing (or nothing!) but it is the children’s reactions to it which have escalated it into a problem. That's where a teacher's coaching and children's social development come in.
From a parent's perspective, it can be difficult to distinguish between true bullying and 'children being children' because the end result of these situations can look similar - that is, an upset child who may feel that others are against them. This is understandably upsetting for any parent and it can lead them to think that their child is being bullied, when in reality, the situation is part of their child learning how to interact within different social structures and contexts.
When a fall-out happens, speak with your child about the reason for the disagreement, trying to get to the basic root cause of the issue. Often this is very minor, and has been escalated by the way in which the participants dealt with it. Also, do keep in mind that children are actually very good at leaving out details which make them culpable (or at least partly responsible) for what happened!
If you feel that there are unresolved parts of the issue, your first port of call is your child's teacher. You can speak to the teacher at the start or end of the school day, or email your concerns. Email addresses for each class and teacher are listed on our Parents' Useful Information page. You can also contact the office. If you still don't feel that the issue has been resolved, you can ask to speak to a member of school's Senior Leadership Team.