It’s perhaps even more maddening than that. Even if all these factors are at play, it doesn’t mean they actually matter all that much to anyone involved. These two coworkers might otherwise really get along and respect each other, but this is one of the games that they are playing with each other.
On the surface, implicitly negotiating over who is more important sounds horribly dramatic, but it’s a game that’s happening constantly among everyone. Usually folks push and pull over some equilibrium point, one person making concessions, then the other, in turns, with the actual hierarchy determining roughly how many turns each person should concede before making a demand of the other. This is where you get dynamics like “he’s a very demanding boss but he cares a lot about his employees” (high amplitude of switching between demand and concession) or “she’s very sharp but also hard to get along with” (doesn’t concede enough to make others feel important).
Concession in this game can be anything, small to large, from being the one who opens the door to let the other through, to offering help during personal problems, to letting someone take more credit on a collaboration.
But, again, these are all played in the implicit layer. They can be raised to the explicit layer by having a “heart to heart”, like “you’re always so kind. I appreciated when you did XYZ”, or “I’d really like if sometimes you did ABC”.