Dual wielding in real life was historically rare. There's a variety of reasons as to why, but all of them can be boiled down to the same explanation: it doesn't work.
Firstly, the weapons that dominated ancient and medieval battlefields were the polearm (spear, long axe, pike, halberd, etc.) and the bow (shortbow, recurve bow, longbow, or crossbow). With few exceptions, the sword was primarily considered a sidearm - something to be drawn when your polearm broke or you were otherwise in a tight spot. Even the famed samurai, known for the katana or tachi at their sides, fought primarily with the bow (Yumi) and glaive (Naginata) in earlier periods, and later with the spear (Yari) and arquebus (Tanegashima). In formal duels, where the sword was more common, the sword was only one of multiple weapons with which the combatants might be armed. Despite not being as glamorous as the sword, the polearm provided several tactical advantages. It had superior range over the sword, and hundreds of soldiers formed into a bristling wall of spears is a significant obstacle, particularly against cavalry. The bow, meanwhile, allowed one to attack from a great distance: it doesn't matter how great a swordsman you are when hundreds of arrows are being fired at you.
Polearms particularly are furthermore relatively easy weapons to get the hang of. The sword by comparison takes significantly more training to use effectively. It's no coincidence that Ancient Rome, one of the few historical civilizations to rely primarily on the sword in combat, was also one of the few with a professionally trained army. Most other states relied on levies. Most importantly of all: they were cheap. Spears and bows are much easier to produce and maintain than swords. Spearheads and arrowheads require significantly less metal to forge, and don't require the same level of sharpening as a sword. These three things (training, cost, and upkeep) were what you were looking for when equipping an army of thousands of untrained peasants.
The point being, with swords already finding limited use on actual battlefields, the idea of wielding two swords at once would have seemed absurd. It would be similar to a modern army deciding to replace all the rifles of its soldiers with dual-wielded pistols.
Even in one-on-one duels, dual wielding has many drawbacks. A potential advantage of dual wielding is one's opponent having to worry about two potential avenues of attack. However, if the blades are long enough they have a tendency of simply getting in the way of one another. To avoid this the swordsman is forced to hold one sword deliberately out of the way, meaning often he attacks with only one sword at a time, eliminating the point of dual wielding in the first place. On the other hand, striking with both blades at the same time makes about as much sense as striking simultaneously with both fists in boxing, and is ineffective for the same reasons: you strike with less power and accuracy, and it leaves you completely defenseless if your opponent dodges or blocks. Nor does dual wielding make for a faster pace of attack; striking first with one blade and then the other is not actually any faster than striking two quick blows with a single sword. Sure, you could use one sword to block and the other to attack, but if you're going to do that why not just have a shield?
This is where most dual-wielding did appear historically: in formalized duels using a rapier paired with a dagger. Since the off-hand weapon was primarily used for blocking, it made sense to have a dagger rather than another sword (less weight, doesn't get in the way of the sword, etc.) Daggers with hooks and special serrated edges were made to make it easier to "catch" the opponent's sword. Ideally one would block with the dagger and simultaneously strike with the rapier. However, even this practice died out after the early Renaissance.
Dual-wielding is seen in other isolated contexts. Native Americans were known to dual wield a tomahawk with a knife or even another tomahawk, but weren't known for fielding and equipping large armies. During the Spanish colonial occupation of the Philippines; civilians were prohibited from owning swords, so Eskrima practitioners developed dual-weapon styles focused on sticks and short knives. Chinese monks had hook-swords and dagger-spikes that were dual wielded, but monks practice martial arts for meditation and fitness, not for practicality, and whenever they had to actually fight on the battlefield, they usually chose to trust more in good old staves rather than exotical blades. European pirates sometimes wielded a pistol alongside a cutlass or boarding axe, but having a gun in one hand that only has a single shot is significantly different than putting a melee weapon in your off-hand, particularly when that gun is already pretty inaccurate so you'd need to be close up to use it.
Any instance of using a weapon and shield is technically dual wielding; while video games tend to categorize shields as "armor," they were historically considered weapons and you were expected to know how to strike with them if you were using them. This is a far cry from using two swords or daggers, however, and a shield's primary purpose was to block and parry.
