Cersei was killing at a young age. The difference between Cersei and Joffrey is that Cersei didn't raise herself. She learned to lie about what happened to inflict pain on those she wanted to punish, although she most certainly made sure they got punished. You can see that in the story the Viper tells Tyrion. Cersei calls Tyrion's wet nurse a milk cow and treats to have her tongue out. This type of vicious behavior, although no one would dare tell Joanna or Tywin, is known among the servants at Casterly Rock and in Lannisport, and it is likely that these whispers from servants to servants is why Cersei was refused as a bride for Rhaegar Targaryen. Looking at the timeline, it strong looks like 1. Tywin and Aerys made plans to marry Rhaegar to Cersei, when both were quite young. Rhaegar was born in 259, while Cersei was born in 266. Most like, since 270, there had been agreement between Aerys and Tywin to marry Rhaegar and Cersei, or at least an understanding. The Lannisport Tourney happened in 276. Rhaegar would have been 17, with Cersei at 10, ideal ages for a bethrothal. Rhaegar can live a happy early twenties doing whatever he wants and then in four or five years, he marries Cersei Lannister, the daughter of the Hand of the King and the wealthiest family in the realm. She is even said to look like Joanna, the woman Aerys wanted more than his own wife. They stage a tourney in Lannisport to celebrate the event and announce it publicly, and Aerys chooses to reject Cersei due to the news of her tendencies, in the same manner that the Tyrells decided to kill Joffrey. He chooses to humiliate Tywin on top of this because he is jealous. It is only AFTER the tourney in Lannisport that Aerys sends his cousin Steffon Baratheon to find a wife in the Free Cities for Rhaegar. This mission fails, and it is now 279, and his son Rhaegar is twenty and unmarried. Due to his public shaming of Tywin, Aerys is forced to look only at the other Great Houses of Westeros for a bride. Lyanna Stark was too young and already betrothed to Robert Baratheon. Jon Arryn has no daughters. Catelyn Tully is spoken for and the Tullys are a clear step down from the Lannisters anyway. There are no Baratheon women, and the Tyrell women were spoken for. This is why Aerys picked Elia Martell, a woman uniquely unsuited to the role of Queen.