From A Separate Peace by John Knowles, what are some key quotes that show Gene's neurotic personality?

The word "neurotic" isn't used in psychology circles so much any more because there are more specific words used to diagnose different mental illnesses these days. The word technically refers to an unsettling of the nerves, or pertaining to nervousness. Gene does seem to be nervous, but more specifically, he is a paranoid, insecure teenager with a newly discovered dark side that he must learn to tame. This dark side comes out as Gene's paranoia and insecurity are pushed to their limits as he inadvertantly breaks his pre-supposed rival's leg. Because the book is written from Gene's perspective, there are many quotes that discuss what he is thinking and how his thoughts expose his paranoia and insecurities. 

In chapter 2, Gene admits to being envious of Phineas. Gene realizes that Phineas can charm his way out of anything, beat anyone at any game, and do anything he wanted in life. Gene says, "There was no harm in envying even your best friend a little"(25). But this slowly starts to get out of control as Finny seems to do one incredible thing after another. Gene's mental status spirals.

For example, in chapter 3, Finny breaks the school swimming record and Gene hits a breaking point with his jealousy. Finny didn't want to tell anyone about the accomplishment so it festers in Gene. Gene says the following:

". . .so I didn't tell anybody. Perhaps for that reason his accomplishment took root in my mind and grew rapidly in the darkness where I was forced to hide it"(44).

This darkness and hiding things builds up in Gene to the point where he can't contain his jealousy and that isn't good for mental health.

By chapter 4 Finny and Gene get into an argument about grades, recreational time, and how each one perceives the other. Gene realizes he has been jealous of Finny, but what really gets his goat is when he says:

"He had never been jealous of me for a second. Now I knew that there never was and never could have been any rivalry between us. I was not the same quality as he"(59).

By this point, Gene is completely riled up mentally and he's energized to go prove himself by jumping off the tree into the Devon river again. Again, not a good frame of mind at this point and it leads to him jouncing the branch which leads to Finny's broken leg.