We already know all witches are hunted and went into hiding. It's no differnt in the future. When she is born, she is hated and abused, and doesn't know why. She's only like... 5... "Leave me alone, I havn't done anything " she'd be saying.

So when she grows up and becomes more powerfull, she seeks to remove SeeD and all those that was mean to her.

There's a ton of info to back this up Here

Some key points include how she says to Squall "so...you're the legendary SeeD member Squall..." And he's all like because he's only just joined, and is the newbie rank. But in her time, in her history books, he's the legendary member.