What exactly is wrong with FFVIII?
I think for the most part, the problems people have with it come down to the fact that it's one of the least conventional games in the series, throwing out basically everything people liked about FF7 before it. I myself liked that it tried to be different instead of just sticking to the same old formula, but that usually doesn't sit quite so well with most people.
To give an example: One big thing is the system of drawing and junctioning spells - basically, the game has no such thing as MP or learning spells, instead you draw spells from enemies, and can then either cast those, or equip ("junction") them to stats to boost them. Problem is that drawing spells is really tedious and you'll probably spend more time doing that in any given battle than actually fighting, especially if you want to collect enough powerful spells to get the biggest stat boosts. It also means that casting magic is kind of pointless, since you're casting from the stock you're using to boost your stats, which obviously means your stats go down as you use magic - just get your physical attack high enough and use that instead. Basically you end up with little variety in battles beyond drawing spells, attacking, and occasionally using summons. The actual numbers behind junctioning are a bit silly, too - very early on you can get 99 Curaga and junction them to everyone's HP, giving you like 4000 HP in disc 1 and making it near impossible to actually die to anything until about late in disc 3.
The story comes in for a lot of criticism too. It's basically a really convoluted mess, especially towards the end - the actual ending scene is basically a complete mindscrew and I've yet to meet anyone who actually made any real sense out of it (at least not without getting into spoilers). There's also Squall himself - most people don't like him being moody and highly introverted (I personally found him much more interesting than Cloud, but I didn't like Cloud at all so that doesn't say much).
I still like the game better than FF7 despite all its flaws, so I'm really disappointed at how it constantly gets short shrift while FF7 hogs all the limelight. I'd say it's the more deserving of a remake - it has some good ideas in theory, that just need some refining to make them work better (or just work, in some cases).
Also, as Red pointed out, Laguna exists and brings with him his glorious battle theme, which is one of the best tracks in the entire series:
The whole soundtrack is pretty good, Uematsu was on fire when he was working on this game.
This post is probably a bit of a mess and not as informative as I'd like it to be, but I'm on mobile and it's hard for me to type something like this on a phone. So it'll just have to do for now. :p