This is only one of the scenes where Noel argues with Snow. There are more times when Noel mentions that he hates Snow, calling Snow an idiot and things like that. But why so much? Why does he have so much hate directed towards Snow? (it has nothing to do with Serah)
http://m.youtube.com/watch?v=isdqvI6Yiic&feature=relmfu --- You shouldn't always believe what other people say.
Half of Snow's character is to be there for characters to misdirect their anger and frustration on. The other half is to be irresponsibly heroic. Snow went off on an adventure without telling Serah where he was and was fighting monsters he couldn't win.
Noel is frustrated with those kinds of people, especially since he himself was left behind by Caius, and has watched his entire village slowly die. Watching Snow run at monsters with a nonchalance probably made him flashback tho those issues.