>The root cause of fight is that partners disagree over something that is important to both (likely related to some core value).
If both partners disagree about a core value (and no mutually agreeable compromise is possible), the rational thing to do is either separate or for one party to accept the disagreement and move on. Repeatedly arguing about something serves absolutely no purpose, as there's extremely little chance of one party changing the other's mind this way (as is the case for angry arguments in general). As the Einstein quote goes, the definition of insanity is doing the same thing again and again but expecting a different result.
Stress and sleep deprivation indeed make this more difficult, but these are things that can be eliminated, if not easily: case study, people who aren't sleep derived or stressed (everybody's probably met at least one).
>Self-control and compassion don't make disagreement or bad feelings over important things disappear.
Compassion and empathy make it easier to see why other people feel/think about a matter in a particular way, and hence easier to sympathise with their point of view, which in turn reduces bad feelings about it. Self-control helps us not get angry about things we've accepted (if we haven't chosen to separate, and can't convince our partner to accept our view, then we've implicitly accepted them having their view), as we can make our brain see how silly/irrational it is to get angry about something we've agreed to, reducing bad feelings.
> It does not have to be screaming match, but if you never disagree about things like child raising, it is likely that one did checked out.
I agree disagreement is practically unavoidable, but a disagreement need not become a fight. Getting angry is a terrible way to resolve disagreements. People manage to disagree about things they care about at work without getting physically angry, as they know getting angry will probably harm their case.