The Fall of the Citadel [HL2: Episodes 1 & 2]
At the end of HL2 you complete your assignment, by destabilizing the Citadel in City 17, the Combine throne on Earth. As a result, the Combine's communication network has been taken down, and the Combine forces are fractured and leaderless.
GMan tosses his pawn back into stasis. Gordon is now in hypersleep, as he has completed his job, and he is no longer needed. GMan is about to warp in and transport Alyx when he is intercepted by a group of Vortigaunts. They warp in, rescue Alyx, and transport her outside in front of the Citadel. They pull Gordon out of stasis, and transport him to a location near Alyx. Both of these things happen against GMan's wishes. The Vortigaunts have in effect taken control of Gordon, blocking GMan from intervening in Gordon's adventures. GMan has to resort to kindly asking Gordon to protect Alyx when the Vortigaunts let their guard down to save her life in Episode 2.
The Combine on Earth have lost their primary method of communication with their Combine leaders. In a last-ditch effort, they decide to destroy the Citadel in the creation of a high-energy "super-portal". In conjunction with the creation of this super-portal, the Combine need to send a transmission packet back to their homeworld detailing to their forces how to access it - what amounts essentially to a high level reinforcements request. This process will lead to the deaths of all of the rebel forces and evacuees of the city. The Combine also prepare the remaining Combine for escape via escape pods during the meltdown.
Why do the Vortigaunts pull Gordon out of stasis and place him just outside the Citadel? I believe they want Gordon to stop or at least delay the destruction of the Citadel. They want Gordon to stabilize the core reactor of the Citadel so that the rebel forces and the rest of the Vortigaunts can safely evacuate the city before it is destroyed.
Why doesn't GMan like them doing this? The way I see it, GMan wants that reactor to be destroyed as soon as possible and that transmission packet to be sent, at any cost. Why? Because it seems GMan is trying his hardest to lure the rest of the Combine forces over to Earth. This seems like GMan's plan from the beginning, the reason why he got Gordon to destroy the Citadel. This reason is to bait the rest of the Combine over to Earth so they can be fought on Earth, or so that GMan could distract the Combine while he mounts an attack on the Combine's homeworld. The way GMan sees it, hundreds of thousands of human and Vortigaunt lives will be lost in the destruction of City 17, but if that message is sent, GMan could win an interstellar war. On the other hand, the purple Vortigaunts care more about the lives of the members of the Resistance and the citizens of City 17 on Earth than winning the war.
Unfortunately for GMan, Gordon and Alyx do stabilize the core (or at least, for a few hours) to allow the Resistance to evacuate. Though, in the end, this allows the Combine enough time to send their message, as well as successfully evacuate the Combine escape pods from the Citadel, in a stunning discharge of raw portal energy, leveling City 17. These escape pods are dispersed all over the countryside surrounding the remains of City 17. As a result, the immense super-portal is now operational and is awaiting the opening of another dimensional gateway from the Combine side.
Alyx and Gordon manage to secure two transmission packets from the Citadel. On the first packet are contained the exact coordinates and instructions for the operation of setting the super-portal as a gateway to send troops. The second packet is more intriguing- exact coordinates and blueprints depiciting the location of the missing Borealis freighter. On board is believed to contain a portal technology much more advanced than Black Mesa's.
Despite sustaining a massive attack, aided by a code from the transmission packet, the rebel forces manage to launch a rocket, which in concert with the satellites launched over 20 years earlier during the resonance cascade, is able to shut down the super-portal. The Combine is held at bay, for the time being. However, as Gordon, Alyx, and Eli (unfortunately) learn, the hatched Combine Advisors are still roaming the countryside, feeding on the very rebels that are trying to take them down.
Quelle