McMurphy was angry that Harding, who'd been on the ward since before McMurphy arrived, probably had some idea of what McMurphy's continued antagonizing of Ratched would mean. Remember that Mac said he'd figure out a way to drive Ratched so crazy that she'd lose her temper? Mac's behavior from then on was solely focused on finding ways to defy Ratched's authority. The overarching theme here is that Mac is meant to be a liberating force for the men on the ward, who live a dreary day-to-day existence under Ratched's tyrannical rules.
What Mac is unaware of is that when he was brought to the hospital and started acting so rambunctiously in defiance of Ratched's rules, she recommended to the hospital board that Mac's status be changed to "Chronic". In the novel, the narrator, Chief Bromden, explains that there are essentially 2 types of patients on the ward: Acutes who are only mildly affected by their mental condition; Chronics, who are more severe in their behavior & who, at least in the time period the story takes place in, the 1960s, unable to function in society. Billy Bibbit and Harding are both Acutes -- there is a belief by the hospital administration that they can be cured & returned to society. Bancini is a Chronic, he seems unable to function outside of shaking and saying "I'm TIRED" all the time. Bromden is considered a Chronic because he never talks and the hospital staff believe he is deaf and dumb, which he really isn't.
A few moments after McMurphy confronts Harding about how much he "had to lose" Harding tells him that he's a "voluntary" patient: he's at the hospital of his own volition because he wants to be cured of whatever mental problems he has and he believes Ratched and the other staff can do this for him. Billy Bibbit is also voluntary but is mainly a patient at his mother's insistence -- sometime in the recent past he'd had a breakdown because he'd asked a young woman to marry him & she likely rebuffed, perhaps abusively. Both men, being voluntary, can leave the ward any time they wish & go back to their former lives. Ratched, however, is so controlling that she keeps them believing that they can't leave until she allows it.
McMurphy accepted his transfer to the hospital from prison, believing that life in a ward like this one would be easier compared to prison. However, he'd never figured that he'd be pitted against Nurse Ratched. Also, McMurphy also believes that when his prison sentence was finished, that he'd be let go from the hospital. There's a short scene right after Mac's team's victory at the basketball game where they're all swimming. One of the ward orderlies, Washington, who already doesn't like Mac & has little respect for the patients, pokes him with a pool hook. Mac says he'll see Washington "on the outside" & Washington tells him that he'll be let go when the hospital staff deems it appropriate. The moment is a revelation for Mac, who now understands what kind of situation he's in.