> Pushiness is quality as in "property", but not "quality" as in "the degree of excellence of something."
It's quality as in the degree of excellence of pushiness.
> In this case, lower quality individual bubbles on top, cause other horses don't want to deal with jerks aggression.
That would be a higher quality individual, according to the horses.
> You write about it as if animals were rational systems thinkers and that is just not so.
We're talking about behavior that evolved millions of years ago in crustaceans, the serotonin brain system that specializes in regulating social hierarchies in animals, is still present and functioning today in you and the horses. Attribution of rationality is on your part, and in no way diminishes the effectiveness of the social brain, and the hierarchy which it encodes.