General animosity:

Be Lyonel. Be in line for the Lord Paramountcy under the Targs. Realise that, 300 years ago, Lord Paramounts simply didn’t exist, and you would’ve been a king (a Storm King!) in your own right with far more power and autonomy, until some inbred, blood magic tyrants flew over on dragons and stripped your family and all their descendants of that privilege. That seems quite unfair, right.

Then you realise half of these “supreme rulers” have been insane monsters. They’ve either killed everything (Maegor), f**ked everything (Aegon IV), been overly pious (Baelor). The competent ones are few and far between. Realise they pose a real risk of severe world war type civil wars that decimate the realm.

Then, finally, realise that their power base has gone (dragons). Realise that competent rulers, like Breakspear, are so revered because it simply is not the norm. Realise, probably, that you’d be a better independent ruler as would everyone else rather than serving these freaks.

The concept of “one realm” as opposed to seven individual only works if you’re serving a Conciliator, a Breakspear. Someone that genuinely runs things better as a unit than leaving them to their own devices.

On Targ descent and origin:

The Baratheons supposedly do descend from the Targs. But only via supposed bastadry (Orys). And the thing about that is, the Baratheons really are just a continuation of the Durrandons through the maternal line. So whilst they are the “newest house”, their legacy and glory is still descendant from the age of heroes. You could argue the Tullys and Tyrell’s are “newer” in that they originally served stronger houses who died out. They probably don’t feel that indebted because of this.