??? their interests are not in conflict with ours?
They wanna fvck; we wanna fvck. They want to have fun; we want to have fun. They want to meet new people; we want to meet new people. They want to connect; we want to connect. They want to be desired; we want to be desired. They want someone to be with; we want someone to be with. Shall i go on for another 5 paragraphs, or do you pretty much see the picture by now?
EVERYONE'S interests are in conflict with everyone else's.
Not really because everyone wants the same exact things: love, happiness, adventure, security, wealth, health, friends, etc. These aren't things that you can gain by taking them away from others, but things you can gain by giving them to others. Hence, everyones interests are perfectly aligned. Think about it. How do you gain love? You give it. Can you feel love if you take it away from another? How do you gain friendship? You give it. Can you gain friendship by taking it away from someone else? And so on...
it can be considered a game with winners and losers and opponents?
Everything can be considered a game, and the opponents can be just about anyone we imagine. Ourselves, our friends, co-workers, society, environment, ideas. You can label anyone an opponent, but labeling them that will only make them opponents in your own mind and in your own life. Some brothers see eachother as opponents and steal from one another, but are all brothers opponents? Some coworkers do the same, but are all coworkers opponents? So on...
you speak of the grand scheme that men (the concept) and women (the concept) need each other... well, for a great deal of men (actual) and women (actual), they're not finding any part of that philosophy true in their lives.
If you're a low-quality mate, few will want to mate with you. This doesn't make them evil, this just means that you're low-quality. It isn't personal.
and if it's not a war, there's a helluva lot of history, philosophy and literature that finds evidence of shooting.
You can have war between anyone, at any time, over anything. All it takes are a few people with a skewed sense of reality. Their ability to involve others in conflict doesn't mean that all other members of the two (or more) parties always are, or ever should be in conflict.