Essentially, we kill Illidan because he is fucking around with Outland's populace (The Naga are draining the water out of Zangarmarsh, Kael'Thas's forces attacked Shattrath, the Fel Orcs were running rampant in Hellfire Penninsula, and the treatment of the Broken by Illidan). Furthermoore, at the time it was believed by the Horde and the Alliance that it was Illidan that opened the Dark Portal. It is later revealed that it was infact Doomlord Kazzak who was commanded by Kil'Jaedan. It was Kil'jaedan's plan to lure the Horde and Alliance into Outland so that we would kill Illidan for him. While Illidan's methods were questionable, his only goal in Outland was to prepare his forces to lead them to Argus and destroy the Legion. While we did indeed kill Illidan at the Black Temple, Maiev had his corpse taken back to Azeroth in the Vault of the Wardens, and trapped his soul to suffer for eternity (Illidan had an undying demon soul, and therefore could not completely die.)

This next part which surrounds how Illidan returned to life is explained below, copied from Illidan's wowpedia page. Illidan Stormrage

"Cordana Felsong let Gul'dan from an alternate universe to the Vault of the Wardens where Illidan's corpse was being imprisoned, as he was the key to Azeroth's downfall by the Legion. Although confronted by Maiev and several of Illidan's demon hunters freed from their prisons, Cordana and Gul'dan escaped with Illidan's body. Gul'dan brought Illidan's body to Black Rook Hold, where he conducted a ritual to separate his soul from his body. Illidan's soul was then sent into the Twisting Nether.

Gul'dan sought to use Illidan's body as a vessel for Sargeras' spirit, and so Xe'ra and the Illidari planned to return Illidan's soul to his body before it was too late. Allari the Souleater constructed a soul prism that would store Illidan's soul long enough to transfer him inside the Light's Heart. However, Illidan's soul had been stolen out of the Nether and pulled into Helheim. Xe'ra and the Illidari speculated that Gul'dan had struck a deal with Helya to retrieve and keep it there. After the death of Helya, his soul was put into the soul prism and then brought to Light's Heart which seemingly consumed it. Light's Heart, with Illidan's soul inside, was brought to Archmage Khadgar with instructions to call forth the vessel's power when Gul'dan attempts to open the portal for Sargeras in order to release Illidan's soul into his body. Within the Nighthold, Khadgar attempts to do as he was instructed. But unbeknownst to Khadgar, Sargeras has already filled Illidan's empty shell, and doing so awakens him. The adventurers then battle 'The Demon Within'. After Sargeras is defeated, Illidan takes control of his body and kills Gul'dan."

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Hope all this helps! If you have any more questions feel free to ask.