Nurse Ratched: Well, anyway, this is no way to proceed about this.
One of the things that makes Nurse Ratched so powerful in this movie is the way she never loses her cool around the mental patients. This cool demeanor always makes her look more like an adult than them. But over time, it becomes clear that this tactic is horrible for the men's self-esteem because it makes Ratched seem like their scolding mother.
Sefelt: Maybe he'll just show Nurse Ratched his big thing and she'll open the door for him.
The more McMurphy gains influence in the mental hospital, the more he teaches the other patients to think like him. In other words, he teaches them to think of Nurse Ratched as just another woman, and they joke about her doing whatever McMurphy wants—if he shows her his penis. It's a crass moment, yes, but the fact that minor character Sefelt says this shows us just how far McMurphy's influence extends.
Cheswick: Miss Ratched. I'd like to ask you a question please.
Charlie Cheswick gets fed up and decides that he doesn't want Nurse Ratched treating him like a child anymore. But he doesn't realize that Nurse Ratched has the power to send him off for shock therapy if he gets out of line. And that's exactly what happens.
Nurse Ratched: Mr. McMurphy. The meeting was adjourned and the vote was closed.
Nurse Ratched never bends when it comes to what McMurphy wants. As far as she's concerned, there's only one way of dealing with men like McMurphy, and that's teaching them who's boss.
McMurphy: You're going to pull that henhouse s*** now, when the vote…
In moments of intense frustration, McMurphy reveals just how annoyed he is that he has to submit to the power of a woman. Using a word like "henhouse" in this context refers to the fact that McMurphy thinks of Ratched as a mother hen, or a woman who's gotten a taste of power and now plans on abusing it. Could we attribute McMurphy's rebellion entirely to sexism? Maybe not. But it definitely contributes to it.
McMurphy: That f***ing nurse, man. […] She ain't honest.
McMurphy says exactly what he thinks of Nurse Ratched when he's alone with the male hospital doctors. He expects to get sympathy because they are men, but finds out that the men respect Ratched very highly. He figured that bros would stick together, but that's not what happens. We're betting Nurse Ratched exerts a certain amount of power and control on the staff, too. Maybe everyone—doctors and patients alike—is afraid of crossing her.
McMurphy: Well I don't want to break up the meeting or nothing. But she's something of a cunt ain't she doc?
This line shows McMurphy's lack of respect for women more than any other in the movie. He thinks it's fine because he's among men, so he calls Nurse Ratched the c-word for always bossing him around all the time. He doesn't seem to realize that he's in the hospital for a reason and Ratched is in charge for a reason. In his mind, a woman should never have this kind of power over a man.
McMurphy: She likes a rigged game. You know what I mean?
The thing McMurphy dislikes most about Nurse Ratched is her ability to rig situations in her favor. Every time McMurphy thinks he's outsmarted her, it turns out that Nurse Ratched is one step ahead. McMurphy finds it hard to deal with this constant humiliation, and his only resort in the end is to try and strangle Ratched.
McMurphy: The best thing we can do is go on with our daily routine.
McMurphy blames Nurse Ratched for causing Billy Bibbit to commit suicide by shaming him for having sex with a woman. But even after Billy has died, Ratched takes no responsibility. She just tells the men to go back to their routine. So McMurphy totally snaps and tries to kill her.
Nurse Ratched: Now you feel better, don't you?
Sefelt: Yes, ma'am.
After being attacked by McMurphy, Nurse Ratched seems to act extra kindly to the patients of the mental hospital. It's not clear whether the attack has permanently changed her personality. Maybe she's just playing it cool until she regains her power. Either way, it's safe to say that McMurphy's lobotomy has changed him a lot more than the attack has changed Ratched.