Are people's interests naturally in conflict?
No. People's genuine values and interests are not naturally in conflict. They can appear to conflict in a narrow context, especially when people want the same exclusive thing, but human life is not fundamentally dog-eat-dog. In the broader context, rational people prosper through production, trade, friendship, love, learning, and voluntary cooperation, not predation.
The key word is genuine. A person's real interest is not whatever they happen to want in the moment. It is what actually supports their life, happiness, self-esteem, relationships, and long-term flourishing. A win-lose arrangement usually collapses under a wider view: The exploiter degrades his own character and relationships; the self-sacrificer burns resentment into the relationship; the manipulator destroys trust; the person who "wins" by faking reality becomes less fit for life. In that sense, all supposed win-lose or lose-win situations are really lose-lose.
This does not mean people never want mutually exclusive outcomes. Two people may want the same job, the same university seat, the same scarce item, or the same victory in a sport. But those are conflicts over concretes in a limited context, not proof that human interests are metaphysically opposed. In the broader context, you do not prosper by getting a job someone else is better suited for, displacing a more qualified student, forcing an owner to sell you an item when someone else values it more, or winning a contest by anything other than superior performance within the rules. Competition can be value-producing when it reveals merit, raises standards, and lets people pursue excellence honestly.
The practical test is this: What kind of interaction is this? If it is voluntary, honest, reality-based, and value-producing for both sides, there is no necessary conflict. A training partner can want progress, and you can want progress. A spouse can want connection, and you can need sleep. A business can need profit, and customers can need value. However non-obvious it may be, the task is to find the context where both sets of legitimate values can be respected, not to assume we live in a zero-sum world where we'd better exploit others before they do the same to us.
This is why rational self-interest does not mean indifference to others. It means refusing both self-sacrifice and predation. Make the tradeoff explicit: "I want dinner together, and I also need to train. Can we eat at 19:00?" If the other person treats every standard you have as an injury to them, the issue is not mutual interest. It is control, poor boundaries, or a demand for unearned sacrifice.