At what moment does Gene betray Finny?A Separate Peace by John Knowles

In Chapter 3 of A Separate Peace,
Finny persuades Gene to jump from the tree; when Gene loses his balance, Finny's hand
quickly shoots out and he grabs Gene's arm, saving him from falling.  Later, Finny
persuades Gene to ride their bicycles to the beach.  There they swim in the ocean, but
the waves are too strong for them and they are knocked around.  Yet, Finny enjoys
himself, even convincing a bartender to give them beers by displaying some forged draft
cards.  That night Finny tells Gene,

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"...after all you can't come to the shore with
just anybody and you can't come by yourself, and at this teen-age period in life the
proper person is your best
pal."

This show of emotion
"nakedly" stops Gene from telling Finny the same thing.  Then, the next morning, Finny
declares that he has a great rest.  With renewed energy, Finny tells Gene, "You never
waste your time.  That's why I have to do it for you."  Gene feels that Finny tries to
prevent him from studying so that he will not be better in academics than
Finny:

He
minded, despised the possibility that I might be the head of the school.  There was a
swift chain of explosions in my brain, one certainty after another blasted--up like a
detonation went the idea of any best friend, up went affection and partnership and
sticking by someone and relying of someone...in this world--whom I could
trust.

...i found a single sustaining thought....You and
Phineas are even already.  You are even in
enmity.

Feeling that Finny
has deliberately set out to wreck his studies, Gene is further angered when Finny
announces that Leper will jump from the tree and they must attend.  When Gene objects
because he needs to study, Finny tells him to stay, but Gene misinterprets Finny's
motives and insists upon coming.  However, as they walk, Gene begins to understand that
there is no rivalry between them because he himself "was not of the same quality as he
[Finny]."  Gene becomes jealous of Finny.

Once at the tree,
Finny suggests that he and Gene do a double jump. They climb the tree and walk out onto
the limb. As Gene takes a step Gene's  "knees bent and [he] jounced the limb." Finny
falls with a "sickening, unnatural thud."  Then Gene describes
himself,

With
unthinking sureness I moved out on the limb and jumped into the river, every trace of my
fear of this
forgotten.

Clearly, Gene has
betrayed Finny.  He has betrayed his belief in Finny's friendship, his admiration of
Finny, and, most of all, his respect for Finny.  Gene becomes bitter from a false sense
of betrayal to himself, then acts cruelly from a petty sense of inferiority to
Finny.