(Spoilers Extended) The HOTD show does an excellent job at showcasing the generational trauma
The show story of the Greens is one of handed down generational trauma that has made them all so fucked up.
We see hints that Otto himself didnt have a particularly great upbringing or life prior to his rise as Hand of the King. Hes a 2nd Son who stood to inherit nothing as Daemon aptly put it. When a lord reaches the age of majority, a 2nd son becomes an unwelcome competitor. They lack the security that heir has. So Otto rose off the back of his own merit and luck in politics, but we see in season 1 in his conversation with his brother he defaults to the subordinate. Politics was his only path to power and security, so he raised his children with politics in mind. The loss of his wife also made him colder undoubtedly.
And Otto's parenting essentially broke Alicent. All but forcing her into a marriage she didnt want at a young age, ruining her relationship with her best friend, traumatizing and scaring her that her children will die if Rhaenyra ascends. Essentially it made it near impossible for Alicent to love and relate to her children as she emulated her father's own parenting style.
Its best illustrated when Alicent tries to open up to Otto and he shuts her down with 'I dont want to hear it'. And then in the next scene Aegon is broken over Jaehaerys death and Alicent walks away instead of comforting him.
The great tragedy of Alicent's children? Is they really never stood a chance. Alicent had them because of politics, not love. She struggled to relate to them or love them as she was constantly fretting and agonising over their threat to Rhaenyra and her young age made it difficult to feel like a mother.
Viserys was extremely neglectful because his guilt and trauma over Aemma's death made him openly favour Rhaenyra to an extreme. Rhaenyra is his child of love, but also his desperate attempts to make things right with Aemma's memory. His first wife and love died screaming at Viserys order, he never recovered from it. His illness also caused his capacity to be there for his children to degrade.
So....is it really any wonder how these kids turned out? Aegon the lazy fratbro prince, Aemond the burgeoning sociopath so starved for affection he pays a woman to be a maternal figure and Helaena....so ignored and misunderstood that even when she speaks of the future nobody understands or believes her.
The saddest part of it all? There were signs at least Aegon and Helaena might break the cycle. Both clearly cared deeply for their children. Albeit Aegon favoured Jaehaerys, and Helaena favoured Jaehaera. But there is no doubt both loved their children and made sure to let the children know they were loved. Perhaps with time Aegon and Helaena could have healed themselves and raised two children with the love and affection they never truly got. But now? They will forever be broken by what has happened. A war forced upon them by the evils, sins, mistakes and ambition of their older relatives.
Tl;Dr Rather than looking at things like team sports, try appreciate the story the show is trying to tell with the Greens. How the generational trauma carries down across generations. Its beautifully tragic.