I personally am in the camp that Gman is Combine himself (high level, possibly unknown in the ranks of the mooks), so far in the grand scheme of things if everything had gone his way the Combine would have been out ahead.
So a mysterious man delivers something to Black Mesa which just so happens to open a portal storm, he also commissions the army to do a coverup (if I recall correctly from the manual of Opposing Force), almost assuring SOMEONE would encounter and kill the Nihilanth. Nihilanth dies, portal storms start and Combine come out and eat our faces in the 7 hour war. On top of that the Administrator went through a “great deal of trouble” to get the sample and was “pushing to get results that day.” Is it possible the Gman offered him that cushy position at the head of humanity in advance for allowing the incident to occur and that the great deal of trouble referred to him accepting that he was effectively selling humanity out?
Then the two people who proved the most capable threats (Shephard, and to a greater degree, Gordon) are put in holding, probably so they couldn’t foul up the war itself. Everything seems to be running according to plan and then they hit a snag… a resistance has formed but they can’t find the leaders for the life of them, even the basic members are well hidden in society. One thing they know, they idolize one Gordon Freeman who was said to have fought off droves of aliens before.
So the Gman arranges a shadow deal with Eli Vance, pretending to sell Gordon to the resistance while really working on a bigger plan. Yes, he knew the presence of Gordon would spur a full on rebellion, get them out of the woodwork so to speak. On top of that he managed to blow the Citadel. This sounds like a huge DETRIMENT at first, until we found out some juicy information. If they blew the Citadel they could send a packet and warp in another full invasion fleet. The resistance is out in the open, a huge force is coming through and… game over?
“But wait…” you say, “Gordon is going to stop it!” Yes, he is NOW. But let’s review, the G-man tried to put him into holding at the precise moment things would be at the worst for the resistance, the packet would be going out and the resistance would be in full sight, easily destroyed, and straight in the path of any giant fleet that may appear with their capable hero completely gone. The Vortigaunts, even if they didn’t know Gman’s plan or what he was (which they could very well, they clearly know SOMETHING. Maybe he pulled the same trick on them?) sensed something was amiss and rescued Gordon, who the Gman clearly knows is capable. Was he merely mad because he lost a very good business tool? Possibly, but I think it was more likely that he was well aware of the gravity that a Freeman running around could easily throw a monkey wrench straight into the plans he carefully crafted and that that particular extraction point was all but necessary if he wanted the finalization of humanity’ s enslavement to go smoothly.
Edit to add: This does still leave open a few holes, like why did he bargain with Vance the first time to save Alyx? The answer is that I’m not sure. Perhaps he figured having a non Combine-aligned human trusting him would be a good trump card? Maybe he really didn’t think she was of no practical use to anyone and planned from the start to have her assist Gordon if some rebellious tendencies formed? It is a good question, but not one that I’m sure invalidates the theory.