As an "FFXIII hater" who has conversed with many others of his kind, here's why people tend to hate the game:
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-The battle system is doled very slowly over time.
By the time you get to Chapters 9-10, you consistently have a three-member party and all characters have access to all six roles. At that point, the battle system is, in my opinion, actually pretty good. There were several later boss battles where I thought, "Oh...now I see...THIS is what they were going for with the battle system." But for the 8 chapters (~20 hours) up until that point? You're usually stuck with a two-member party and even when those two-member setups you don't have access to Sentinel (in the case of Sazh/Vanille) or Sentinel AND Saboteur (in the case of Lighting/Hope). What this means is that, for me and several others who have grown up with Final Fantasy and/or JRPGs in general, that the first 8 chapters are boring, repetitive time-sinks. Most of the battles are too easy and take too long. In short, FFXIII doesn't have a difficulty curve so much as it has a difficulty wheelchair-ramp.
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-The story wasn't presented in a way that was palatable to a great many in the target audience.
Every other game in the Final Fantasy series that came before had a story that was fully presented within the dialog/cutscenes; Final Fantasy XIII doesn't present all of its necessary exposition within the dialog and cutscenes.
Most other games that have a "datalog" (The Clan Primer in FFXII, the Codex in Mass Effect/Dragon Age, the Jiminy Journal in Kingdom Hearts) don't make it required reading to understand the story; Final Fantasy XIII requires the player to read the Datalog to understand the story.
When you consider each pair of facts side-by-side, it's not hard to see why the story has so many haters. Those that couldn't be bothered to read the Datalog didn't understand the story at all and were alienated from it (this was me when I first played the game), and those who felt that they shouldn't have to read it to understand the story, but read it anyway, resented having to do so (this was me after I finished the game; I can't tell you how many times I would come across any interesting story bit and ask myself, "Why didn't they include this in the cutscenes?!).
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-The game was extremely linear.
If the above two problems had been fixed, I would've liked the game, maybe even loved it. Despite my antipathy towards it, I can recognize that it had so much potential. But with such a repetitive and dumbed-down battle system in the first 8 chapters and a story that didn't engage me, the series of tubes that is FFXIII's "maps" really started to feel monotonous, even to me, a person who doesn't at all mind linear games.
I really liked FFX. Because I liked its story and battle system, the linearity didn't matter to me. If FFXIII had given me a battle system that wasn't "meh" for the first 20 hours and story that drew me in, I wouldn't have taken issue with the linearity at all.
At the same time, the linearity was a big problem for a lot of people.
Just look at the series itself: FFX's linearity had a large amount of haters back in its day as well; when you consider that FFI-FFIX had fully explorable world maps and FFX does not, that actually makes sense. Then, coming off of FFXI (which was an MMO) and FFXII (which was set up like an MMO in its openness and freedom), FFXIII was even MORE linear than FFX. For those fans who really liked "exploring a world" as part of why they liked the older Final Fantasy games, FFXIII's linearity was bound to draw criticism.
And then, when you look outside the series, for people who prefer Western RPGs, FFXIII is pretty much everything that they DON'T want in a game.
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I hope this helps you understand why the game didn't work for me and so many others.