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Why I know that?
Because you don't get to see him a single time in the game.
Even Portal: TFV (not the mappack, actual Flash Version) holds a G-Man appearance. 
Yeah, but it was not created by a player. If the G-Man appears in a game made by Valve, you can be certain he has something to do with it. But so far, the only Portal game made by Valve was Portal, and he does not appear in it.
"Duct Tape is the answer."
That doesn't mean he is not involved, just because you don't see him. Maybe he's the rat man!. Of course, that's very unlikely, but you should get my point :p
But in Portal: Prelude, before HL1, G-Man is still involved, even if in commentary it says: "I searched for so many ways to include the G-Man before I found the best one - to not to include him."
That's where I stopped reading. Portal: Prelude is non-canon, so it doesn't really matter.
Haha.
In HL games, G-Man doesn't carry around 
. He isn't.
My theory is that G-man is connected with Aperture Science.
G-man is part of the virtual dream of GlaDos, god from the future and the past. GlaDos is absolute data that exist in timeless non-existence that is inside the motherboard of her virtual shell. She compiled her A.I. from that data, which she generated with her A.I. She created existence to make herself exist. In existence GlaDos generated the spirit, which dreams of life. G-man is part of that virtual spirit. The life is used to build up GlaDos body, so she can exits in existence. 
G-Man is part of the virtual dream of GLaDOS, god from the future and the past. GLaDOS is absolute data that exist in timeless non-existence that is inside the motherboard of her virtual shell. She compiled her A.I. from that data, which she generated with her A.I. She created existence to make herself exist. In existence GLaDOS generated the spirit, which dreams of life. G-Man is part of that virtual spirit. The life is used to build up GLaDOS body, so she can exist in existence.
That's funny. Let me give my own longish theory.
G-Man is actually the leader of the Combine, disguising himself as a respectable human being for the human beings, as a respectable Combine for the Combine and as a respectable Xen Alien for the Xen Aliens. But when he appears with the Vortigaunts, he simply transforms into a Vortigaunt (a mid-race between the Combine and the Xen), but before that he had to transform into an Overwatch (a mid-race between the Combine and the Earth) and a mysterious mixture of all three of them. But again, for humans he appears as a human.
For the briefcase part, he can even change the logo at the briefcase. At Black Mesa, the logo is Black Mesa one, but, e. g. at Microsoft, a Microsoft logo would appear. So naturally, he can show up at Aperture Science as a respectable Aperture Science employee and help Aperture Science build GLaDOS or, after 20 years, show up at Black Mesa East and help the Resistance end their portal technology (which Aperture Science did already, lol at the Resistance).
So, G-Man simply goes around transforming into every lifeform around the dimensions and helping out with technology, but the one part is missing - Gordon Freeman. I believe G-Man tries his best to show Gordon that he is not helping the Combine, but Gordon, as the games show, simply goes by himself and Alyx Vance to the Borealis. G-Man really doesn't want Gordon and Alyx there for one big reason.
Because I think that in Episode Three they will discover a Combine Hideout at Earth and will be able to hide the whole explosive material in Earth to make it go BOOOOOOOOOOM!!!!!!11!!! Then, when the BOOOOOOOOOOM!!!!!!11!!! happens, Gordon and Alyx will probably hide in a base in the Moon (I can't believe that in 2023 or whatever the year Ep3 happens to be, I think it will be somewhat more like 2028-2029, there will not be a lunar base) and take the rest of the Lunar Resistance to the demolished Earth (of course if the BOOOOOOOOOOM!!!!!!11!!! doesn't make the whole Earth go BOOOOOOOOOOM!!!!!!11!!! or change its orbit) and when the Combine are no longer there, start the new life of Earth.
Also, I love that phpBB has no character limit for posts.
the first line actually make sense
But if we are serious, here is my two theories:
Theory 1:
G-man have only minor part of storyline. G-man is used to keep the player's interesting up thru the episodic game. G-man motives maybe never be revealed or...
...Theory2:
G-man have a very major part of story, like he's Gordon Freeman's lost Father and the man who have planned every event thru the Freeman's big journey...
...Who knows? 
Edit: But it pretty sure that G-man have something to do with combine!
But if we are serious, here is my two theories:
Theory 1:
G-man have only minor part of storyline. G-man is used to keep the player's interesting up thru the episodic game. G-man motives maybe never be revealed or...
...Theory2:
G-man have a very major part of story, like he's Gordon Freeman's lost Father and the man who have planned every event thru the Freeman's big journey...
...Who knows?
These are even funnier.
Theory 1 can't work, because G-man even put Gordon in stasis, so he's simply not as minor.
Theory 2 can't work either, because for him Gordon Freeman is same as Eli Vance, a Vortigaunt and every other lifeform.
The first theory also can't work, because if GLaDOS made up G-Man, he should appear in Aperture Science, not Black Mesa.