I have seen quite often that many people consider young Alicent to be too sensitive and just an envious/jealous girl. Well...
Daemon almost killed Alicent's brother at the tourney, (he was much younger than him). Gwayne was so badly wounded that even the maester had to personally visit Otto and warn him that his son will live.
Otto and Daemon's relationship has always been tense. Daemon allows himself to insult the memory of Otto's dead wife, in front of EVERYONE at the council.. And I remind you, mother's death is the same trauma for Alicent as for everyone's beloved Rhaenyra whom everyone loves to justify her behavior with the death of her mother. But no one talks about Alicent, even tho she also lost her mother. Alicent loved her very much and she still misses her, praying every day at the sept. Do you think she doesn't know what kind of relationship her father has with Daemon? She knows what a terrible person Daemon is, what frightening violence he is capable of, but she is silent and smiles because he is a prince, he is the brother of the king, and uncle of her best friend. She always has to be silent, polite and patient, just like her father.
Imagine what Alicent felt when she found out that Rhaenyra had slept with a man like Daemon? Betrayal. No, it's not just envy that her "friend" has privileges, it'sdisappointment. To make matters worse, Rhaenyra lied to Alicent, she SWEARS BY HER MOTHER'S GRAVE AND DEATH that she IS TELLING THE TRUTH. Mother. Little Alicent values her words, she values the memory of her mother, she is still grieving, and she believes Rhaenyra.
She even refuses to believe her own father, the closest and dearest person in her life. And for what? Eventually she becomes the reason why her father is kicked out of the Red Keep in disgrace, depriving the status of the king's right hand. She defended Rhaenyra's honor, she justified her, and was left absolutely alone again. No mother, no father.
She feels the bitterness and pain of loneliness in the court, and then this feeling doubles because what she did turns out to be a huge mistake. Her best friend is a liar. From Alicent's perspective, her best friend hooked up with a man who had been at enmity with her father all her life, almost killed her brother, and after Rhaenyra smiles at her as if nothing had happened, and shamelessly scatters words, the consequence of which is the departure of her father.
But yeah, for some stupid reason of course "she's just jealous girl" and nothing more.