I think that Jack feels that with unrequited feelings he has towards Ana and that 'rejection' adds to his feelings she is responsible for him 'loosing' everything because Christian bought the company. So it's that jealousy of "if I can't have anda then no one else can".
He wants to kill ana to get back at him coz carrick and grace adopt christian and not him. He thinks if it was him then ana would' ve been his its all revenge and jealousy
Jack never actually says that he wants to Kill Ana. He is a sick individual who thinks that Christian Grey messed up his chances at a good life. Therefore he wants to have,or destroy what Christian has including Ana.
Jack wanted to kill Ana, first; because she was Christian's life and we all know how much he hated Christian as when they were in the Foster utama the Greys picked Christian instead of him. Second; she wouldn't give him sexual advantage and she was the reason he was fired.
