First of all, the junction system is utter crap. You can break it so hard, so fast it's not even funny. My characters all had well over 3000 hp and OHKO'd most enemies before I even fought Edea. I like uber cahracters, but not that soon.
Worse still, the game actively encourages you not to play it. Gaining exp is bad. In fact, I'm sure many people found the game almost unbeatable because they overleveled. Stupidest leveling system ever.
Also, the characters are weak. Squall goes from pretty hard to like to still being pretty hard to like, yet he has a pretty significant change of attitude. If he were real, I wouldn't want anythign to do with him before or after that. And worse still, the change isn't gradual or sensible, it just sorta happens out of the blue. If you go past him, everyone else is pretty much an archetype taken to the limits, and so either people love the characters or they hate them, and there's not much middle ground. Even my favorite characters have traits that I can look at and say "yeah, I know why people might hate them."
Then there's the story. It was pretty much hopeless. It started off fine enough, though hardly FF-like. Then it decends into pointless stupidity. The same orphanage? Save the girl from dying in space? Stop the missles? Blech. Nothing was original, and every aspect was done better by another game at some point in time, let alone what books can do for a story. Take for example the torture scene, which wasn't that good. In "Wizard's First Rule" the main character gets tortured, and the torture scenes there delivered. I didn't like Squall and wanted to see him really get tortured, and the most that happens is he gets shocked a few times. Richard (frome WFR) was tortured for days, or even weeks, and the way he got out of it wasn't anti-climactic like in FF8.
Also, there wasn't a singular villain to despise. In VI you had Kefka and in VII you had Sephiroth. Both were pretty badass as in their own ways, and both did plenty of things that could lead the player to hate them. In FFVIII it kept switching. Often times the bad guy was just someone being possessed and you jsut sorta felt bad for them. And then when you finally do come across the villain, there's not much oomph to it. There was no time to build a hatred, and winning didn't leave a sense of fulfillment.
So it didn't play well, the story was weak, the characters were simply archetypes personified, and it didn't deliver on any of the promise it had. What's there to like, really? There are dozens of RPGs that surpassed FF8 in any given aspect a player may care about, and there are a handful that easily surpass it in every aspect.