We saw that the Argonians have joined the Ebonheart pact in the second era.
Well, if they alliance the Nords, and the dunmer, why the hate for each other 2 eras later?
Here's my theory.
As the Ebonheart pact destroyed the other three sides, and marched on Cyrodiil, something went wrong. The Argonians were assigned the role as reinforcements should anything go wrong.
And things did go wrong. Ambushed by the Daggerfall Covenant on their march on Cyrodiil, they lost all their men, and were placed with letters in their corpses about "betraying" the pact, and secretly giving away their tactics to the Aldmeri Dominion.
The Nords then found them, and were disgusted by their actions.
Thus the war during the 2nd Era came to an end - the Nords started their hatred of the Argonians, and the Aldmeri Dominion, whilst the Daggerfall Covenant won due to their brilliant thinking.
Ulfric Stormcloak then continued this tradition.
Anyway, just my theory.