How we cite our quotes: (Line)
Quote #1
MAY: What am I supposed to call him?
EDDIE: A "guy" or something. If you called him a "guy," I'd be worried about it but since you call him a "man" you give yourself away. You're in a dumb situation with this guy by calling him a "man." You put yourself below him. (168)
Eddie is sizing up May's date through her word choices in describing him. Clearly, he's trying to figure out whether to feel threatened—and for now, he's decided Martin is no threat because May calls him a "man" instead of a "guy." We're not sure what the difference really is, but it seems to be some kind of macho logic about how cool Martin is likely to be.
Quote #2
"Anybody who doesn't half kill themselves falling off horses or jumping on steers is a twerp in your book." (171)
May picks up on the fact that Eddie is trying to paint Martin as somehow less macho or manly than him in his own mind with this "guy" vs. "man" distinction. Apparently, Eddie is quite the manly man cowboy, and anyone who isn't at that same level isn't likely to get his respect.
Quote #3
"It was about whether or not you're actually a man or not. Ya' know? Whether you're a "man" or just a "guy.'' (391)
Later, when Martin has actually arrived, it seems that Eddie might be trying to throw him off balance by telling him about his argument with May about what kind of dude he was.