I understand why they hate talos, but I still haven't figured out why they hate the blades.

The Blades doubles as a Talos Cult.

The Blades identified the Thalmor as a threat, and took action against them. There was a shadow war between the two groups for some time before the Great War, when the Thalmor revealed just how much over the Blades' heads they were.

The Fourth Era began without a Dragonborn to lead the Empire, paving the way for the Mede Dynasty to take over in 4E 17. In the second century, the Blades realized that the Thalmor posed a great threat to the Empire, and to any Dragonborn should they return. The Great War between humans and elves began in 4E 171, when a Thalmor emissary demanded the surrender of the Empire, and when they refused, dumped the heads of 100 Blades agents who had been operating within the Aldmeri Dominion on the floor, along with the demand that the Blades be disbanded. Later, the truce known as the White-Gold Concordat, signed by Emperor Titus Mede II in 4E 175, decreed that the Blades be disbanded. Furthermore, the Thalmor were given free rein to hunt down Talos worshippers, a privilege they employed to eliminate the surviving Blades one by one. Massacres occurred at the main Blades fortresses, such as Cloud Ruler Temple. By 4E 200, only a handful of Blades remained on Tamriel, with the Penitus Oculatus having replaced them as the Emperor's bodyguards

I got this from http://www.uesp.net/wiki/Lore:Blades

Edt: Fixed the messed up post.

They were the only competant mannish spy organization left, and they had been performing counter-espionage against the thalmor's agents.

Personally, I just find that word "mannish" terrible.

Human would suffice, or any other option.

by mannish I mean mannish aligned. I'm sure the blades had non-humans in their ranks.

The Blades were the "eyes and ears" of the Empire which happens to be the Dominion's rival. I think the rest is self-explanatory.

Yeah, the Blades are Talos worshipers and they were spying in Aldmeri land.

The blades serve Talos and Talos is a heathen god in the eyes of the Thalmor.

Blades work for the Empire and are the main threat towards the Thalmor.

They used to like the blades very much. They were best friends even... But then they met Delphine and now they hate them. It's understandable.

As said before, the Blades serve Talos and the Dragonborn Emperor, and they were pretty much the ones hindering their plots up until the Great War. They are, to the Thalmor, the physical embodiment of everything they hated, so...they hate the Blades.

The Blades serve the Emperor, And Thalmor hates Emperor.