Most people's first arguments are fighting with their parents. When someone is getting emotional during a debate they are most likely dredging up emotions they felt towards mommy and daddy.

Stop reading Freud

Yet somehow, saying "calm down, I'm not your dad" rarely diffuses the situation when my wife is mad at me.

That feels like a big stretch. By that logic, you think about what you were looking at during your first wank every time you achieve. And thank the heavens that isn't true.

I get where you're coming from, and I think it's a good shower thought.

I don't, however, agree with it.

What's missing is that parents aren't always the first argument, and that disagreements don't inherently result in anger.

Where it does make a basic kind of sense is that we do learn our coping mechanisms petty early on by observation. If we're surrounded by people that argue regularly, and do so heatedly, that's the structure we absorb as being the default. If you're among people that disagree without arguing, then you pick up a different default.

It's the same as any social interaction rules, we pick them up over time. But the emotion of anger isn't inherent to disagreements. Not even for little kids.