I was asking this question myself for a very long time. But even though I enjoyed it, I can sort of understand the hate.
The most prominent complaint by far is the linearity. Objectively, many, many maps are straight and narrow corridors. Heck, I once saw some video that called it "Final Hallway XIII." I'm one of those weirdoes who doesn't mind the linearity- in fact, even if they gave me more options, I'd probably still make a beeline for the plot- but this didn't sit well with the FF fanbase at all. Seems to me like they expect more wiggle room than a narrow path. You have to get many, many hours into the game for it to finally drop you off in the Archelyte Steppes for some free roaming.
Then, the battle system. Each battle can take a lot of patience, and the worst fights take a massive amount of persistence. Mess up on one little thing, and the last 20 minutes of progress you made on some SoB is for naught. I dunno where I found the persistence that let me beat so many of those fights, looking back on it.
Also, I got a little feedback from a family member on the game: he couldn't really get into it because cutscenes kept hijacking the gameplay every other encounter. He couldn't make any progress without the game interrupting him. His other complaint was the battle mechanics; again, they were just a little too slow for him. ATB didn't let him take care of things quick enough.
I'm pretty annoyed that the sequels ever became a thing, to be honest. XIII had an ending that I was okay with. There was no reason to mess with it or continue it, and yet they did. Just. Why.
For realsies.
I have hard time trying to fully comprehend the entire structure of character development and what effects does that have towards the story.
*shifts uncomfortably* Well... character development doesn't just affect the story. It's
part of the story. It's a way to show that the events of the plot have an impact on something, as well as a way to both present and resolve conflict. XIII has a habit of focusing really close and personal on each individual character, so character development becomes even more important than usual. In fact, a great deal of the conflict in the early game comes from these sorts of things (Lightning's less than cooperative attitude, Hope's beef with Snow, Sahz's problem with his son being a Cocoon l'Cie, the list goes on).
So, if that stuff is done poorly, you don't have a very good story, do ya?