Hiashi vs Gai
Sorry, but I need to put my two cents in here.
Honestly, I think that in any universe, Hiashi is at -least- 15 % jealous of Gai.
This man came from a line of emotionally stunted classists. I can imagine that he didn't have much to do with Neji until after the chuunin exam wherein his nephew aired their family's dirty laundry. I find it hard to believe that his guilt and station didn't drive a huge wedge between him trying to cultivate a relationship with Neji.
Then he realises, well shit, I fucked up and my nephew hates me. He does try to at least somewhat set things right (in the few ways this man born from generational trauma can think of). He also knows that he's ruined his relationships with his daughters, too. He's starting to understand that the way he was raised, and the way his kids were raised, was at least a little bit wrong.
So, where does he go from here? Neji is the easiest to fix because he is everything Hiashi wanted in an heir; the strong, stoic, genius. He helps him cultivate those attributes and then sits back and pats himself on the back because 'hey, look, I'm doing a thing! Look how great my nephew is!'.
Enter Maito Gai.
You cannot tell me that Hiashi's pride does not take a significant hit the first time he sees Gai and Neji interact. Gai is the most insightful and caring person in all of Naruto. He has a bond with his kids that is hard to replicate because he does what a lot of the other sensei's won't do; he shows physical affection and teaches with positive reinforcement. Under his tutelage, all three of his students flourish spectacularly. Whereas Team Eight and Ten got stagnant and hit their ceilings at a certain point when it came to their sensei's training, Team Gai far surpassed everyone's expectations of them.
Now, I'm not saying that the other teams didn't get stronger, but a lot of that is attributed to getting older/ finding new people to help them train. Kakashi's whole team fucked off to do this.
Meanwhile, Gai's team only got closer. They all have physical fighting styles, they are the fastest team in all of Konoha (this is said a few times, no I'm not gonna run around pulling up receipts, just google it), and they develop strategies and attacks that use all three of their strengths and weaknesses. Their motto is literally 'stronger than yesterday'.
Gai excels in everything that Hiashi lacks. His kids can come to him rain or shine and everyone knows he is literally their adoptive dad at this point. Hiashi has not only decades of awkwardness to work through, but generations of classism that will always keep him and his nephew apart until he fixes things. Sure, he makes him the 'lead strategist' in the war, but he had years to abolish the branch family seal after Neji surpassed Hinata, and he didn't.
This is not even starting in on the fact that Maito Gai is literally the strongest person in the whole series. Who better than him to teach these kids? He may use taijutsu primarily, but he also taught Tenten how to seal, create seals, master weaponry, and hone her other attributes to make her well-rounded. He can fight the sharingan blow for blow because of Kakashi, plus he's mastered the gates so he has an expert's knowledge on chakra pathways, kinesiology, and dealing with a genius. Everyone thinks that he was hand picked for Lee. Nah, fam, he's the only one who could handle -any- of his kids. None of them would have flourished under other senseis. In fact, I'd say that any of the kids would have done better under Gai, but not vice versa.
I just have a lot of feelings about Hiashi resenting/admiring Gai and the way he handles his kids. Neji 'touch-starved' Hyuuga has had more hugs, praises, tough love, and heartfelt conversations in one year training under Gai than he probably had with his whole family in his entire lifetime. Yes, Neji had to get bitch slapped by Naruto to get the point driven home, because he was a little snot when he was thirteen, but I bet you, hands down, he would have gotten there anyways with Gai as his sensei. Yes, he thinks Gai is ridiculous, but you cannot tell me that he does not respect the ever living hell out of him. Like. Please. Neji's a genius; he'd be an idiot not to.
And BECAUSE he's a genius, there's a moment when he must have realised (or started to realise) that he couldn't just fall back on his abilities or intellect and coast along. Gai made him realise that he had to put in the work or he would have hit his ceiling long ago.
I bet you, a thousand to one, that Neji taught his uncle something because of the way he trained with his sensei. How much would it piss him off that someone who doesn't even have his kekkei genkai can know how to make it better?
I digress. Can someone write me a 'Gai adopts Neji' story? Like IDK how, but somewhere in this world it needs to happen and I need to be able to read it.
For now, I will just headcannon how Neji is the kid from a blended family where he's passed back and forth between parents with 50-50 custody.