They're satirical representations of the negative qualities most prominent in each quadra. It's like a caricature. In a positive social setting, this is great because it means that they're comfortable communicating with each other in any which way they please, not worrying too much about their words being taken to heart, hence the light teasing. The problem lies in them carrying this same attitude over to negative social settings. They just fly off the handle (extratims, mainly) and expect that you'll forgive them for being cunts to you for potentially no reason, even if they ruin your social standing in the process, which they assume you'll jump back from just as they naturally would. All quadras are guilty of this self-centered thinking.

I think that's where the Alpha-Gamma clash becomes most apparent. Alphas talk to talk. Gammas talk when they have something to say. If an argument breaks out between the two, Alpha types fire away until they feel better (aka "everything's out in the open") but Gamma types stay quiet, and if they do say something then they usually mean it, and where an Alpha type leaves that interaction feeling a cathartic release of sorts, Gamma types internalize the irritation they experienced during that interaction and it sticks with them for a LONG time, hence why they're prone to grudges/revenge/etc. And I don't think Alpha types are above, "public executions," (especially ILE, jaysus christ almighty). Alpha is thinking, "Just call me an idiot!!! Please!!! Let's get this over with already!!!" whereas Gamma is thinking, "You're an idiot but I'd rather you just shut up. Goodbye."

This is probably why Alphas tend to, "love by touch, not by words", because nothing they say really means anything. Rooster Teeth podcasts are a fantastic exemplar of the Alpha quadra in action. The positive manifestation, that is.