tl;dr: The Dunmer historically treated the Argonians as sub-human, using them for slave labor, and there have been multiple wars between the two races. Although nearly every other race on Tamriel has treated the Argonians pretty badly, the Dunmer just happen to be right next door, so the conflict between them is heightened moreso than any other race.
The Argonians have, in general, a very strong dislike for almost every race on Tamriel, in particular the Mer races, for much the same reason that so many real-world cultures dislike each other: invasion and subjugation.
As near as we know, the Argonians were already firmly established in the Black Marsh when the mer first arrived on Tamriel from Aldmeris. (This is true of all of the "beast" races -- the Khajiit were apparently quite advanced when the Altmer first arrived, for example.) However, the Argonians were not what the mer considered 'civilized' -- they were not literate, for example, in the sense that mer thought of it. (They didn't grasp the concept of the language of the Hist that the Argonians used.)
Because of the very harsh climate of the Black Marsh, the Argonians were largely left alone by the mer and men that populated the rest of Tamriel. However, they didn't escape entirely unscathed. Some examples from in-game lore books:
were sent to Black Marsh as refugees or prisoners
- Also in the Pocket Guide, and getting to the heart of the matter, was the first true invasion of the Marsh by the Empire:
A very successful enterprise of bandits and thieves had long been exploiting the swamplands of southeastern Tamriel, a convenient location to the riches of the Empire, where one could disappear without recourse. The coastline along the east of Topal Bay had become notorious for acts of piracy, and in 1E 1033, the Empress Hestra demanded the head of the most infamous of the brigadiers, "Red" Bramman.
The Argonians in the interior swamps of Black Marsh were skittish, and little wonder, as the contact they had with men from the outside was from the like of Bramman and other brigands. Imperial civilization was, to them, rape, pillage, and slavery. As the Cyrodiils pushed deeper into their land, trying to settle it along the pirate routes, they encountered stronger and more violent resistance with each incursion. Once the pirate menace was dealt with, the First Empire was generally content to leave Black Marsh to its native inhabitants.
This already sets up a strong distrust of outsiders for the Argonians, who were subsequently left alone for most of the 1st and 2nd eras. Occasionally, Argonians did leave the Marsh (as can be seen in the Elder Scrolls Online, where Argonians can be found in most major cities) but like most of the Beast races, they were subjected to incessant racism and abuse by the "higher" races.
Eventually, though, the rest of Tamriel began to make it's way into the Argonian's territory. Again, according to the Pocket Guide, it was nominally a part of the Second Empire, and Tiber Septim also brought the Black Marsh into his Third Empire. Unfortunately, this exposes a lot about life in the Marsh to the Dunmer, who controlled the bordering province of Resdayn/Morrowind. In particular, the climate and environment of the Black Marsh was one of the few places on Tamriel more harsh and dangerous than that of Vvardenfell, making the Argonians especially suited to work the farms near the ash mounts. This, combined with the Dunmer's existing belief in their own superiority, led to the inevitable mass slave raids. (Even as part of the Third Empire, which outlawed slavery, Morrowind's agreement with Cyrodiil allowed them to keep practicing legal slavery within their province).
This kicked off a series of intermittant slave revolts and wars between the Dunmer and Argonians over the next few years, with the Argonians and Dunmer trading the bordering territories of their provinces back and forth. Even after slavery was formally outlawed in Morrowind, the Argonians held a grudge, and when the Dunmer society began to collapse after the events of Morrowind, and then the rest of the Empire after Oblivion, the Argonians even took to invading Morrowind and nearly capturing it's capital city.