Yeah. Not who he is but what he does.
Gman is a higher power who "hired" Dr. Freeman. He holds his contract which is "open to the highest bidder." It doesn't mean that Breen could buy the contract away from Gman, it means he could buy it from Gman. What I mean is that Gman is simply the man handing out the contracts. Dr. Freeman is sort of like a mercenary working under a sort of "mercenary hiring service." Gman does not decide what Gordon is going to do next, that is decided by the people who hire him. That's why Gman said "if and when your time comes around again." He did not know when he would have to use Gordon again because it's not up to him.
Spoiler Warning from this point on
I also think that Breen was the first person to "hire" Gordon. Now why would he want Gordon to come destroy the citadel when he's working for the combine? If you were paying attention in HL2, it was Breen who surrendered to the combine. He wanted to ensure the survival of the human race, and for a while it appeared that he did ensure their survival, but when it became apparent that the combine were eventually going to either turn every human into a combine, a stalker, or a bloody pulp, Breen realized that he had to do something. He already knew about Gman and "bought" the services of Gordon Freeman. That's what Breen was referring to when he said "your contract was open to the highest bidder." He payed to have Gordon come and strike a blow to the combine, and he did that by destroying the citadel. I'll get to what they "pay" with later.
I believe that the next person to "hire" Gordon was Eli Vance. He was the head of the rebels and was the highest bidder after Breen's death. He hired Gordon for Alyx's safety. This gets a bit complicated because at the beginning of Ep. 1 Gordon is taken out of stasis, not by Gman, but by the Vortigaunts, who are apparently working against Gman. The next time you are contacted by Gman, is when the Vortigaunts are healing Alyx. He asks you to ensure her a safe passage to White Forest. That is why Gman "plucked" Alyx from Black Mesa in the first place. He knew that Eli cared about her and would "pay" for her safety. She also turned out to be a good help to Gordon, and she also allowed Gman to talk to Gordon when she was injured, and it also allowed him to relay a message to Eli.
To help prove my point, I'm going to go over some other facts. Both Breen and Eli made references to Gman. They both were heads of very powerful organizations, and they both wanted the humans to survive, though Eli also wanted them to be free. They both would have reasons for hiring Gordon, and this is the most important fact. They are both dead. This lead me to believe that the "payment" for someone's services is your life. Once Gman had fulfilled his part of the contract, meaning that Gordon had completed the mission in this case, he takes your life. Breen had the most valuable life to give at the time, he was the highest bidder. The next highest bidder was Eli. Who knows how many other offers he has received. He said he had some "interesting offers which he wouldn't ordinarily contemplate" from people who's lives were valuable. Now the difference in Eli's and Breen's death's are that Gordon killed Breen, but advisers killed Eli. It was in Gman's power to kill Breen because Gordon had a reason to kill Breen, Gordon however would not kill Eli because he was an ally. Therefore either when Gordon brought Alyx to White Forest their contract was settled and Gman orchestrated Eli's death, or the advisers were a random event, and now that Gman could not take Eli's life, Gordon now does not have to protect Alyx. The story line of Ep. 3 will depend on who hires Gordon next.
My 0.02 cents.