Yes, I am a total newb. Don't begrudge me that. But will someone please explain to me why 3.5 fighters are so hated? And is there any way to make them better? And what are the better core alternatives?

Core is a bad idea. It's very biased towards casters, and your best bet is just to suck it up and play a caster. Or non-core.

Fighters suck because of...

• Multiple Attribute Dependency - You need str, dex, con at decent levels & int certainly helps some (tumble, balance and so on.)
• Magic Item Dependency - You need to spend a lot on keeping your weapons (note: multiple weapons, since not all creatures are vulnerable to the same metals, damage types or ranges) & armor up to date. The money you spend on such is money you can't spend on covering your weaknesses.
• Prestige Class Dependency - Fighters don't give enough options from level 1-20 on their own. Most fighter builds that can actually be called decent have very little actual fighter in them.
• Lack of options - You can't prepare your fighters against every circumstance, so you'll find that in many combats, the fighter just can't contribute anything significant.
• Just do damage - Fighters only deal damage. Sadly, fights are better won by "save or die", "save or lose" and "save or suck" spells. Fighters are very vulnerable to such.
• Scale badly - Fighters don't gain damage at the same rate that enemies gain HP. By the later levels, fighters can't deal significant enough damage to influence fights. At the same time, they (for all their AC and larger HD) die really fast when attempting to do what they're supposed to do.

Casters do not face these difficulties. Core games, especially those with limited access to magic items, simply don't give the fighter anything near what it requires to be successful in the mid-late game.

What Hyudra said.

Wow, there's been a lot of these threads lately.

The most unbalanced sourcebook in all of 3.5 is the Player's Handbook. Casters reign supreme and muggles pretty much get shafted. Skill-types can contribute, but melee sorts are screwed.

Their biggest problem is that they don't get anything monsters don't get. They just get bigger numbers to hit the monsters with, and their numbers don't scale nearly so fast as the monsters'. Even at some of the early levels, a level-appropriate monster will frequently have more hit die, and subsequently more hit points (with twice as much not being uncommon), more attacks per round via multiple natural attacks, vastly higher physical scores, comparable if not outright superior raw damage, higher attack bonuses due to big physical scores and lots of hit die, often meaning the Fighter's AC is irrelevant, as the monsters will eventually be powerful enough to hit on a two anyways, no matter how much you emphasize AC, and they're big, meaning size bonuses to damage and grapple bonuses that, when paired with vastly superior strength, mean the Fighter, whose job is to get up close and personal, pretty much automatically gets screwed by grappling.

Make a level 7, core, melee Fighter. This is a level 7 melee character, whose sole strength is melee and is supposed to be capable of performing melee as a level 7 being. Now, pit him against a huge earth elemental, a CR 7 melee creature that ought to be a fair fight against another CR 7 melee being. Simulate that fight ten times and look to see if the Fighter wins even once.

Fighters simply don't have the options or the power to do their job against the enemies they're supposed to be able to do their jobs against. In the expanded game, the only ways to make an actual Fighter (rather than a multiclassed character) are very few, and require twinking out on things like uberchargers and spiked chain trippers, which are still extremely niche and easy to shut down, and they require a great deal of work, rather odd characters, and noncore material rather than the class functioning right out of the box and then adapting to fit a character.

Even as low as level 5, you're looking at a pretty grim battle between a fighter and a Fiendish Tiger - DR 5/magic, 5 attacks on a charge, free grapple attempt on a hit (Large size & Str 23 for +10 base chance, can rake as above if they grapple you), darkvision 60' and 6d8+18 hp (About 45). The tiger's got skills in move silently (and a few in hide) on top of 40' movement, so odds are it'll get that devastating charge in.

The fighter has... one attack. 3 feats.

I think I just might understand now.
What would be a good non-core melee choice?

Tome of Battle. Crusader, Swordsage, Warblade. They're the melee classes that work.

Aren't CR's are aimed at an entire party. Not a 1 v 1

A Fighter flexible enough to work at range or melee is going to be able to engage pretty much any enemy.

Let's ignore that other classes will stomp all over the CR 7 for now.

Fighter's can work out okay but we're talking about such a minimalist impact and such a hard playstyle that they just fall behind.

They aren't dependant on anything but your willingness to make them work and to what end. If you want some melee damage monster at the later levels, you're not going to be a 20th Fighter. You don't need to spend hoardes updating weapons or being MAD you don't even need to PrC to function. You just need to play to your actual strengths, and the Fighter's Job isn't to get into melee, the Fighter's Job is to fight. You want to make a Fighter you make a Fighter who can fight and you do it right.

I always liked the class, I know it's largely pointless to play one, but then again - so is 3e.

The last thing this discussion needs is edition-war baiting.

Fighters playing to their strengths would involve hitting things with sticks, by my reckoning. I mean... fighting. It generally involves melee, yes? And they suck at it. So, if not melee combat, what are the fighter's strengths that we're supposed to play to?

CRs work for all numbers.

A CR X encounter is supposed to drain 20% of a level X party's resources; in other words, it's supposed to be easy, and virtually a guaranteed win for the party. An encounter that can single-handedly take on the entire party in one go would be more on the order of CR X+4.

A level X character is (generally) a level X-4 party and as such a CR X enemy should drain 100% of the party's resources, or a 50% chance of victory (read as a reasonable chance of victory).

A level 10 Rogue should be able to reasonably deal with a CR 10 trap, and a level 10 Fighter should be able to reasonably deal with a level 10 melee creature. That's not remotely the case.
Except he can't be good at both. He can suck at both, or be inadequate at one, and either way, he loses. Particularly since other classes (Ranger) can be good at archery in addition to getting actual class features. And if the Fighter goes melee, he fails at melee.
What?

The Fighter's job is to fight, yet the Fighter can't deal damage, can't take damage, can't avoid damage, and can't hold off enemies... what's left? Pick any of those tasks, and there's maybe one or two ways to get it done. Pick all of them, and you fail at all of them. The Fighter can't fight in a meaningful way bar a few niche paths that are extremely specific, and only exist as an optimization tool rather than a character-representation tool.
Leave the baseless insults at the door, if you please.