At the beginning of Edge of Tomorrow, we see through snippets of news coverage that William Cage is a famous PR officer for the military. Shortly after,
we see Cage head into the office of General Brigham, the head of humanity's United Defense Force. He makes it clear that he is inexperienced and that there's no reason for him to be put into combat, but the general forces him into it.
Why is Cage forced into combat? Why is it so important that the head of the UDF needs to get involved?
It's important to have someone present during the battle to record it for posterity. The fully trained combat soldiers would be busy fighting, so none of them can be spared to work as journalists. William Cage is assigned the job instead. His position would be similar to "embedded" journalists with the modern US armed forces, except that Cage has gone through at least basic military training, so in theory he is better able to take care of himself than a civilian journalist.
We aren't explicitly told why the General personally gets involved with this case, but as the question says, Cage is famous as the "face" of the war effort. It is implied General Brigham is annoyed that Cage has become so famous (and lined up a lucrative post-war career) without being exposed to any personal danger, and has decided to do something about it.
We soon see that the General's dislike of Cage is fully justified, when:
Cage objects to the dangerous assignment and threatens to use his public relations skills to turn the public against Brigham when the casualties start increasing from the invasion. But General Brigham doesn't take kindly to this blatant attempt at blackmail and has the impertinent Major arrested.
Source for spoilered text: Wikipedia
In the General's speech about why he is sending Cage to the front lines, he mentions that after millions have died, the world will need someone to blame. Typically, everyone would blame the General (as he is the head of the UDF). His plan to save his reputation post-war is to have the face of the war (Cage) being filmed on the front lines as they win the war.
General Brigham: Operation Downfall, the entire might of the UDF invading from France, the Mediterranean, Scandinavia, relieving pressure in the Eastern front and allowing the Russians and Chinese to push the enemy back and we all meet in the middle, exterminating this Mimic scourge along the way. A lot of good soldiers are going to die tomorrow, Major, and when the smoke clears and the body bags start coming home people tend to look for someone to blame, someone like me. Ideally I'd prefer a different scenario.
Cage: A best selling memoir perhaps? Maybe a career in politics? Off the top of my head I would go with the..."The Sense of Manifest Destiny", "Rags to Riches: Rags Rise Through The Ranks, Born to Deliver". You see people, well, they'd love that sort of thing.
General Brigham: You misunderstand, Major. I didn't ask you here to sell me, I want you to sell the invasion.
However, Cage was in advertising before the war, and is definitely not a soldier. He is not ashamed of this fact, and is rightfully terrified of being put into actual combat. On his way out, Cage tries to blackmail the general. His plan ruined, the general decides on revenge instead. He has Cage arrested and sent to processing at Heathrow, where the Master Sergeant is told that Cage is a deserter that tried to impersonate an officer.
I think Brigham is on some level in on the whole device of the film. In the first shot of his office you can see that the safe with the apparatus in it is already uncovered, and he tells Cage he is wishing for an alternative to the invasion. At this point Brigham has already heard Vrataski and the engineer's story during the whole Verdun ordeal.
Later Cage is surprised when Brigham hands him the apparatus, since he encountered less resistance than expected.
I suspect that this is a plot hole that the writers deliberately left so that it could be used if there was going to a sequel... and there is going to be one, so we will find out soon.
