Alphabet Story

A, B, C, D, E, F & G are parts of a group.
A & B are lovers, but B has turned his attention to C.
B comes on to C, but C spurns him.
B has himself "killed".
D is killed.
An investigation is set up by A.
C acts suspiciously, but can't be proved guilty because she knows nothing.
E is killed.
F & G begin to strongly suspect C, but can't prove her guilty.
A confronts C, but C admits she is now afraid they will all be killed.
B confronts C and admits how he faked his death to be able to have a "new life" with C, if she'll have him, but says he can't do anything now out of fear because he did not kill D or E and doesn't want to be blamed for it.
For the reader, at this point, the two suspects are F and G.
G learns B is alive and threatens to go to the police and have D & E's murders pinned on him.
In a final appeal to B to give himself up, while B and G are together, A is killed.
B now suspects F, while G suspects both C and F.
C is now scared of all three B, F & G and decides to come forward with what happened between her and B, but F confronts her and says he can't let her do that because he wants all the murders pinned on B. F tries to kill C, but B arrives in time to save her.
G arrives to see B saving C's life and together they get F arrested.
What was F's motive?