Character Analysis
Billy has a confidence problem.
That's highlighted by the way he stutters uncontrollably whenever he's asked a difficult question. Billy might have mental illness, but he's also a young man deep down, and maybe just hasn't figured it all out yet.
He's interested in women, as we hear in his story at the group therapy session about how he "brought Celia some flowers and I said 'Celia, will you marry me?'" But when it comes to his attraction to women, Billy also has a deep sense of shame about his own sexuality, which is connected to his relationship with his mother. Nurse Ratched recognizes this weakness and uses it to torture Billy on two occasions, saying, "What worries me is how your mother's going to take this." On the second occasion, Billy is so distressed that he commits suicide.
Mac's Buddy
It makes sense that Billy has a deep admiration for McMurphy, just like the other men on the ward. He admires McMurphy's confidence, especially when it comes to approaching women. He also resists when McMurphy tries to push him into a room to have sex with Candy. His shame eventually gets the best of him and he commits suicide.
But we're left with the sad thought that McMurphy could have helped Billy gain the confidence he needs to live a rich and full life. McMurphy is a guy who isn't ashamed of his sexual urges in any way, whereas Billy has been beaten down by the constant shaming of his mother and Nurse Ratched. McMurphy tries to help him out, but in the end, the Nurse Ratcheds of the world end up destroying both men.