Conflict is a bad thing, and it comes in many forms. But dealing with it isn’t necessarily all that difficult; there’s a useful framework, based on useful two-way communication.
The first, and possibly most important thing is to put yourself in the position of the person you’re in conflict with; try to understand their perspective. If it is based on something incorrect, then you may be able to correct the mistake, but it’s also possible that your view is a wrong one, so teasing out the details can be very useful. Once you think you understand, then reflect back to the person the basis of their position. Something like “What you seem to me to be saying is this – right?” Listen to the response – you may have misinterpreted. This understanding phase is the most important one – and it allows the other person to have their say.
After this, you should try to have your position understood. This can be tricky, because the likely thing is that the other person thinks or believes that they’re right. Remember, they may well be – you don’t have to win every battle. Changing your position is an acceptable outcome. Using words something like “I need you to understand my position here” can be useful.
The third stage, once you both properly understand the other person’s position is to agree a proposal to resolve the conflict. Note that I’m not saying ‘make’ a proposal – the important thing is to agree the way forward. If it’s just opinion, then agreeing to disagree might be appropriate, but if concrete action is needed, then it might not be.
Some people seem to relish combative situations. I know people who play the devil’s advocate, arguing positions that they don’t truly hold. I think the framework I’ve suggested here can still be useful; rigorously analysing someone’s position seems likely to expose their true position.
Of course, you may come across someone who you just don’t get. Someone who’s really not your sort of person. If this is the case, then you might usefully bring in a third person who you both trust to come to a decision. It doesn’t seem to me to be altogether sensible to avoid the conflict; what you need is a lasting resolution.
It’s hard to write all of this briefly; I hope that you get my central message, which is about effective communication.