"I am going to write down some of the history of Harry Penrose, because I do not think full justice has been done to him..."
The novel follows the career of a young officer, Harry Penrose, written from the viewpoint of a close friend who acts as narrator. A sensitive, educated young man, Penrose had enlisted in the ranks in 1914, immediately after completing his second year at Oxford. After six months in training he had been prevailed upon by his relatives – like most educated volunteers – to take a commission as an officer.
Penrose slowly asserts himself; the war takes a toll on his personality, but he begins to live up to his early dreams of heroism. However, his creeping self-doubt grows by degrees; he is reassigned from his post as scouting officer once on the Somme, knowing he cannot face another night patrol, and earns the wrath of his commanding officer – an irascible Regular colonel – over a trivial incident. The colonel piles difficult, risky work on him – remarking to the narrator that "Master Penrose can go on with [leading ration parties] until he learns to do them properly" – and Penrose submits, working doggedly to try to keep from cracking. After a long period of this treatment, by the winter of 1916, Penrose's spirit is worn down; when the narrator is invalided home with an injury in February 1917, his last support is gone. He is wounded in May at Arras – a friend remarking in a letter that "you'd have said he wanted to be killed" – and they meet again in London in November. Penrose has been offered a safe job in military intelligence; he comes within a moment of taking it, but at the last minute resolves to return to France.
Returning to his battalion, he is detailed for a party to the front line by the colonel within an hour; when the narrator arrives six weeks later, he discovers Penrose is under arrest for cowardice in the face of the enemy. It transpired that each time the party advanced, it had to break for the ditches to avoid shellfire, then regroup and move further; after some time, Penrose decided to fall back and wait under cover for the shelling to halt. Seeing a dugout down the road, they make a run for it under shellfire – to find it occupied by a senior officer, himself sheltering from the shelling, who promptly reports that "he had seen the officer in charge and some of the party running down the road – demoralized" and is ordered to arrest him and return. Penrose is court-martialled on these charges, and convicted; the court's recommendation for mercy is ignored, and he is shot one morning, a week later, by a party of men from his own company.
Penrose is presented in a glowing light throughout – "never anything but modest and dutiful; he always tries his best to do his bit" – but, ultimately, is failed by the system. He faces his trial honestly, without pleading circumstances ("The real charge was that I'd lost my nerve – and I had. And I didn't want to wangle out of it like that") but it is clear that whilst he is strictly guilty of the charge ("on the only facts they had succeeded in discovering it could hardly have been anything else") justice, by any sense of the word, had not been done to him.
"...[and] that is all I have tried to do. This book is not an attack on any person, on the death penalty, or on anything else, though if it makes people think about these things, so much the better. I think I believe in the death penalty – I do not know. But I did not believe in Harry being shot.
That is the gist of it; that my friend Harry was shot for cowardice – and he was one of the bravest men I ever knew."

Question: Why is Penrose arrested?
Answer: For cowardice.