I think it's because social interactions are far more complicated than combat.
I know I've snipped the rest of your post, but it was really this sentence that pulled me up short. Is this claim true? I'm not too bad at social interactions, in the sense that I have a family, I maintain friendships, I do the occasional media appearance as a "talking head" expert, etc. And all I had to do to learn how to do that was to live my ordinary life.
Whereas I know nothing about fighting beyond what I see in the movies. I think it would be very hard for me to learn how to fight.
Having done a fair amount of both fighting and social interact, this assertion also interested me. And it’s not clear what the answer is. One problem is that while we learn early and often how to interact socially, we learn to fight much later, typically, and in a much less pervasive way. It’s entirely possible that for modern people social interactions are more nuanced simply because more time and energy has been put into learning that “system”. But are social interactions fundamentally more complex than combat? I’m not sure.
I think the big difference is that combat is easier to break down into actions. For both combat and social interactions, the scene “stakes” are comparable, but whereas we can break combat down into actions which move us towards the goal, it’s less easy to do that with social interaction. Fate has a go with a mental stress track, and D&D4E popularized the idea of needing multiple successes to achieve a goal, both of which are good and helpful ways of making the two closer, but overall combat is much easier to break down into smaller contests than social interactions are.
I’ve taught fighting a bit, and it’s actually not too hard to stop being a novice and start being somewhat competent. You can learn simple blocks and responses fairly rapidly, and it doesn’t take much practice to learn to keep your head in combat and not panic (for me, this is the most important lesson — get used to being hit and don’t let it stop you). Most people are terrible at throwing punches and kicks, and can be dramatically improved in a few hours.
But thinking about going from “normally competent” to “highly competent”, it takes a lot of work for combat. For social interaction, we don’t see formal training as often, so it’s hard to judge. Maybe consider learning to act? My experience of both suggests that combat is more complicated, but I’m a relatively better fighter than actor, so i can’t really be sure.
The one point that does make me feel that combat is more complex is that for social interaction, innate ability is tremendously more important. If you are actively bad at social interaction, it is very hard to become good at it, whereas for fighting, technique has more of an impact and so it’s easier to become good. Of course, to become a star at eithere, you need talent and technique!
Bit of a meandering post, but in summary I’d have to say that IRL, I can’t see a strong argument that either is more complicated. For gaming purposes, it’s easier to make combat more complicated, but not necessarily more realistic by doing so.