So okay, for starters here's why I liked Lightning. She was angry, and sucker punched Snow, who I hated instantly. So she was endeared to me for just being on full rage mode, which was nice. But as of XIII-2, she isn't that anymore at all. The anger is completely taken out of her and so she is, as people have said, bland.
But here is why people don't like her:
FFXIII sucked. It really did. It was a waste of great potential. The battle system was a good start toward being fun, and the world was very pretty, but there was nothing to do except march straight to the end. There were hunts, sure, but no sidequests, no minigames, no extra dungeons, no turning left, right, or back. Just forward, always forward.
To top that off, the plot was easily the worst Final Fantasy plot prior to XIII-2. It, like the gameplay, was a waste of potential. Everyone, Snow included, had the potential to be a compelling interesting character. The idea of six losers having to band together to fight a common curse and save the world sounds nice on paper. XIII's plot, typed up on internet forums can sound nice, but its execution left much to be desired.
Now, how does all this fall on poor Claire's head? Well, Lightning has been made into the figurehead for this game. As the facewoman for the game that is so hated, the negative feelings related to how disappointing XIII was (and it was, considering how hyped we all were for it) become attached to her. She's on the cover of both games, Square ASKED US HOW WE FELT ABOUT HER IN A POLL, Toriyama touted her as the only female protagonist of an FF (sleighting Yuna and Terra in the process), and she has been receiving the kind of publicity usually reserved for people like Mario, who you know, have been around long enough to deserve the hype.
It shouldn't be hard to anyone to see why Lightning gets so much hate these days. She's become the symbol of XIII, and XIII the symbol of what's gone wrong in SE in turn. XIII sucked and Square has continued to act as if it was everything it was supposed to be. There's nothing wrong with liking Lightning. As she was in XIII I liked her, too, but people are upset because she's everywhere now and there's no good reason.
I wish I could find the post where I had explained this better.