Whether it's friendships, politics or relationships, there will always be conflict between you and someone else, at some time or another.
How you choose to work through that conflict is up to you. You don't have to fight your way through it.
For all their testosterone, a lot of men want to avoid conflict - when our instincts are honed towards aggression and physicality, we are trained (by pressures from society as well as pressures we apply to ourselves) to avoid conflict, because that's easier than constructively working through it and has less consequences than punching the source of the problem in the face. Men walk away.
Women, being physically weaker as a general rule, should also avoid direct physical confrontation (you'd think) but there are a few who think men will never strike back, and resort to physical violence because they think a one-sided physical fight will result in their victory.
But for the most part, women avoid physical altercations and successfully deal with conflicts through other means.
Men could definitely learn from this. It is an area that is sorely lacking in the average mans emotional growth and development.
Conflict resolution relies on a few necessary first steps, and the acquisition of a few key skills.
First, men need to be more aware of their emotional states. They need to understand when they are angry, especially if they are too angry to deal with an emotionally fraught conversation. Mens words tend to be blunt and harsh, lacking the subtlety and pointed barbs of a womans cutting comment. Mens words, especially when angered, can cause bruising collateral damage. You want to avoid this. And that means you need to have a very good handle on your own emotional state. Walking away is not always a bad thing, but your partner should know that it is temporary and that you will return to deal with the issue when you're calmer.
Secondly, you should know the structure of the conflict, and what a good resolution looks like.
Conflicts usually come about because of misunderstanding, miscommunication, or a misalignment of goals/ideals. It should not come about because of a difference of opinion. Everyone is entitled to their own opinion. If you think your conflict is because your partner has a different opinion than yours, then you need to look again.
Misunderstanding : Make sure you both understand each others point of view. If your partner says that a person is attractive, do they mean that they want to sleep with them? Do they mean that they are looking for something other than you? Are they making a harmless honest comment without realising that it preys on your insecurity? Or are they responding (perhaps aggressively) to a compliment you paid to someone else?
If the conflict is over some philosophical point - do you both understand the meanings of complex words in the same way? Clarify your point. Make sure that your partner can articulate your point of view in a way that you agree with, before they explain why they think differently. And the same for you - explain as clearly as you can what your partner is saying, and if they disagree then YOU have not understood their point of view. Listen, and try again.
This is your opportunity to learn from each other.
Miscommunication : Make sure you and your partner listen carefully to what the other person is saying, and avoid the critical mistake of filling in blanks because you assume that you know what your partner is thinking. Listen to what they say. Listen to what they don't say. Don't assume you know what was in the gaps of what they didn't say, and don't argue about what was not said. Give them the benefit of the doubt. If there are two ways to interpret something they said, and one of those ways causes you offence and the other does not.... do not assume they are trying to offend you.
Misalignments : Some will be trivial - where to go for holidays next year? Bermuda? Grand Canyon? You can calmly discuss the pros and cons, and decide together to either pick one of your options or compromise on a third option you both find satisfactory. Each conflict is not extant in isolation though. Even if your points about scuba diving in Belize are incredibly persuasive... if this is the tenth conflict in a row that you will have won, perhaps it's time to just give in - to maintain the belief that your relationship is a two-way street.
Some will not be so trivial - is it the right time to move house? Have a child? Go back to school? Quit your job? See a marriage counsellor? Let her mother move in with you?
Here the shape of the resolution is important. Neither one of you will be happy with the eventual outcome. In order to resolve a serious misalignment of values, someone is going to have to go against some deeply held belief or desire. Maybe you really really want to change a job. But if you do, you'll have to spend time retraining, and you'll become a single income family for a while. Maybe this will involve financial penalties. Or postponing having a child.
The main resolution you're looking for is not that one person is a winner and the other is a loser. You want the relationship, as an entity, to be the winner.
Compromise in cases like these, is painful. And the first question you should always ask is - is this issue more important than the relationship itself? If it is, you should be clear about that. If for example, you're more concerned about being married as a status, than you are about staying with your partner... they need to know this. If you're desperate to have a child, even if it's not with your current partner (who doesn't want a child ever, or for the moment) then you need to need to express this.
If the resolution involves one person getting what they want, their partner might want to place conditions around their acquiescence. Such as "You can look for another job if we first save up 6 months of mortgage payments in case you find it hard to get another job in this market."
Or "I'll support you as you finish college, but you have to support me when I go back to do a Masters" Give and take is how you make an unpalatable choice more bearable.
Just remember that shouting and fighting over the issue, however dearly held your point of view, is almost certainly going to wound the relationship itself - perhaps irreparably.