Elizabeth thinks Abigail wants to kill her because Abigail desires to be with John Proctor and sees Elizabeth as the main obstacle in her way. Abigail wants Elizabeth out of the picture, believing that if Elizabeth is executed for witchcraft, John will be free to return to her. This belief is fueled by Abigail's jealousy, desire for power, and her manipulative actions in the Salem witch trials, including accusing Elizabeth of witchcraft to eliminate her and take her place as John's wife.
Elizabeth is aware that Abigail's motivations stem from their shared past—Abigail had an affair with John Proctor while she was their servant, and when Elizabeth discovered this, she fired Abigail. This rejection, combined with Abigail's obsession with John, leads Abigail to fabricate accusations against Elizabeth, aiming to have her executed and thus remove the obstacle between Abigail and John.
In summary, Elizabeth believes Abigail wants her dead because Abigail wants John Proctor for herself, and getting rid of Elizabeth through accusations of witchcraft is Abigail's means to that end.
