FF13's script is horrible, Recursive. The game assumes we know what all the terms are and does little to ease the player into the game world. Most of the intimate story details are hidden in the datalog. The game has a lot of potential plot developments that are left untangled, random, or have extremely poor resolutions. The party has no goal for more than 80% of the game, character intentions are vague and completely left open, villains are underdeveloped and make pathetic boss of the chapter appearances akin to Sailor Moon, the world of cocoon and pulse have zero sense of culture, especially compared to games like 6, 7, 8, 9, 10, and 12.
Not understanding people's problem with the story and notably the characters (particularly Vanille and Snow) sounds like some really cute naivete. How anyone can NOT be annoyed by Vanille's mannerisms I don't know.
That being said, I'm replaying the game now and I'm on chapter 6, Sunleth Waterscape. The game is far more enjoyable replaying it than I felt about it the first time, especially since I turned off auto-battle. Now I'm remembering that through the poor gameplay/story pacing and complete absence of level design, there's a great game in here somewhere.