In A Separate Peace what is significant in the rebirth motif at the beach in chapter four?

This concept of rebirth, which is alluded to through a reference to Lazarus at the beginning of chapter four, symbolically mirrors Gene's transformation of feeling for Finny.  Before this point, he was envious, a little bit resentful and suspicious, but after the beach incident, his feelings crystallize into true emnity.  After the beach incident, in chapter three, Gene starts to really resent Finny, and to feel almost hateful towards him.  He imagines that they are in competition with each other, fighting for top dog, and that Finny, through his distractions, is trying to keep Gene down.  Before this chapter, he never had such blatant, war-like thoughts about Finny, just generalized feelings of discomfort.  After Finny tells him that Gene is his best friend, Gene can't return the compliment, because he

"was stopped by that level of feeling, deeper than thought, which contains the truth."

And, that truth was that he resented Finny, and almost hated him.  That disdain crystallizes in the next chapter, as a sort of rebirth for Gene.  After he realizes this, and concludes that Finny is out to get him, he can finally be himself again, study, be academic, and do well.  It was an eye-opening experience for him.

The kicker is that we aren't sure that Gene's conclusions about Finny were correct; Gene comes off as a petty, cruel-minded, selfish creature, and we are still rallying with Finny.  The incident at the tree solidifies that feeling, and Gene will have to spend the rest of the novel coming to terms with the fact that he was probably wrong.  I hope that those thoughts helped; good luck!