The way I understand it, let's say you start with a ruling patriarch (or just generally the guy at the top). Now this already isn't easy enough to explain as he probably has brothers, and if he doesn't, his father probably had brothers, and his grandfather probably did as well. Now what I'm asking is, when this guy has a son, that son continues the rule, but I'm also aware that in a derbfine, that the son's brothers would also inherit and gain some measure of rule (as chiefs in their own right), and their kids and so on.
Now what I'm confused about is....well families can get pretty large. SONS (plural) go on to have SONS (plural) and so on. Now I know there's one specific line throughout (firstborns) who are entitled to rulership, but my understanding is that other sons can also found their own chiefdoms, but.....chiefdom over who? Eventually you can end up with so many people that....like, who are they chiefs over? How far from the main bloodline do you have to go before you are NOT allowed to form your own chiefdom? How far do you go before you're no different than a commoner (like say your great, great, great uncle was chieftain by birthright, are you counted at all at this point)?
I'm aware genealogy was extremely important to the Celts, but at some point you'd end up with vastly large families, and they can't ALL rule (there was only so much land really). I'm currently reading something about this, but the book is big with lots of complex concepts and it's taking me forever (also the author seems to have treated it as a given that everyone within a derbfine rules to some extent, so I'm not getting much explanation.....or maybe I will when get to the relevant part, but it's a big book and every sentence has me stopping to see if I understand it correctly).
You're forgetting that these guys formed the warrior class so had a good chance of being killed in battle. There was also a high mortality rate amongst people in general back then and high child mortality. Also, many younger sons of nobility entered the religious orders.
That said, I remember reading an anecdote by an Englishman (forget who) travelling in the highlands who said that there were impoverished men who were treated with respect because of their ancestry. I'm not sure if the Highlanders used the derbfine concept exactly like in Ireland but they had something very similar.
The clan concept (Ireland and Scotland) though was like you say. As many men as possible with a shared name suggesting a shared eponymous ancestor. Some were at the top, some lower down but all respected members.
The derbfine was what, four generations of a common source so it wasn't everyone. Eventually you'd get men at the bottom while the pool for choosing the next chief would come from the current derbfine which is men with a common great grandfather.
The concept of fine is why the political party Fine Gael named itself such - the Irish Race.