Conflict is a normal part of life. Indeed, without conflict there often isn't progress.
Relationships that don't have conflict aren't tested, and tested relationships are often stronger in the long term because people have experienced conflict and have developed ways of dealing with it.
A simple analogy is the stress on a rope: you would not sell a piece of rope without subjecting it to some tension to make sure it's robust enough.
The Directory of Social Change was once planning a senior level restructure when it became apparent that two members of the team both assumed that one of the new roles would be theirs. Both insisted that we stop our plans because one refused point blank to report to the other and we would end up losing one of them. An observer would have noted that there were classic signs of conflict occurring.
It was tempting for me to step in and sort it out, but I did nothing for a week. In that time, the two individuals got together, had a chat and came up with an innovative solution that was better than the original proposal.
It is common, particularly at senior level, to think we have to sort out conflicts, but my experience is that it is usually better to give people the space to work it out. A conflict managed well can result in new ways of thinking and doing.
It's not the avoidance of conflict that should be our goal as leaders; it's how we manage it so that it becomes a progressive force.
When conflict occurs, try to keep the protagonists focused on what it is that they or the organisation are ultimately trying to achieve.
Allow people to disagree, and to be heated if necessary. Make sure it does not get personal but is focused on facts, not personalities. Step in if behaviour is becoming inappropriate or is verging on bullying.
Draw in others, if appropriate, so you hear different points of view.
If it is a conflict over a decision, be clear who makes the ultimate choice.
Stay out of it yourself. Your role is to ensure that both sides get their say. Notice and point out areas of common ground that both sides can agree on.
Don't feel that compromise is the only way. It may be that compromise leaves you with something weaker. If the decision goes one particular way, however, be clear why that is the case.
People need practice in conflict resolution. Avoiding conflict does not help those skills to develop.