(repeating my previous post with a few edits and corrections)
Although we all know that Kael'thas and the Blood Elves dumped the name "High Elves" (and I still agree that any self-proclaimed High Elf prancing around Silvermoon deserved to be mugged for not taking the name that honors the fallen High Elves), they still tend to the Quel'thalas traditions, heritage, and its culture. They own Quel'thalas, Silvermoon, and the Sunwell and they are willing to defend them - as well as the appointed leaders' ideals, they are the true heirs to the title of High Elves and they are closer to the High Elves than the ones in the Alliance. To be a High Elf is to wield magic efficiently, as seen in Blood Knights who command the Light - compared to... High Elf Paladins who need faith to wield Light scratch that it's now forbidden anyway
The (Alliance) High Elves on the other hand, have abandoned their own kin in their time of need and chose to side with their enemy. They no longer indulge in Blood Elf stuff and they chose now to live in Human, Dwarf, and Night Elf lands, they basically set aside the nobility and the elevated status that defined them. They are now more like Wildhammer Elves or "Commoner Elves" than actual High Elves.
Now, why did they chose to fight for the Alliance? They were exiled? Lor'themar made amends for them to come back and they still refused. They didn't want to kill Alliance nor be on a genocidal/omnicidal faction? They could have been simply become neutral like the Kirin Tor or Argent Dawn/Crusade mediators who would settle at least to try and prevent civilian casualties, even Vereesa's husband and the people closest to Garithos' New Alliance Remnants themselves are neutral and are vouching for the Horde. They couldn't stand the Horde? They could have simply stayed in Quel'thalas or made themselves cleanse Ghostlands to be at least useful. But nah, to the enemy they went, while the Blood Elves were suffering in Quel'thalas for 5 years they were enjoying their selfish lives in Dalaran and human lands, doing yoga instead of helping the Blood Elves cope up with their addiction.
And then they further sealed off their legitimacy for Quel'thalas the moment they committed the Purge of Dalaran - they were pretty much eager to kill Blood Elves and they made themselves the enemies of the state (but then again it happened for gameplay reasons because you can't just put the Blood Elves on the Alliance anyway)
Blood Elves are the real High Elves, and the High Elves today are posersQuel'dorei? You are peasants playing at nobility, all too willing to mingle with lesser races that dilute your bloodline. You are unworthy of the name high elves.
(and this is coming from someone who was an Alliance-biased pro-helfer)
(but although I would really love a unification of Vereesa, Umbric, and Mordent's Highborne in Eldre'thalas and make it their new stronghold with Alleria as their leader; Tyrande should really allow them at this point to bask in their Well of Eternity as well)
- - - Updated - - -
to be fair it's not Garithos why the Blood Elves are on the Horde, but because the Alliance refused aid for years until TBC and the only thing that came for them was the Night Elven saboteurs; I wouldn't count Jorad Mace - he was most likely acting on his own
the only ones nowadays who were really affected by Garithos are Rommath and a few Magisters, the Illidari, the Scryers, (and the San'layn if they ever would rejoin their kin)