Because telling Watson is the opening move in her "game".
She reveals herself to Watson that she is Sherlock's sister....so he can pass it on to Sherlock.
Of course, she's insane so her methods are open to question and, naturally, Sherlock still has to force Mycroft to confirm it but her end objective is to drag Sherlock into her web and torture him herself....with the whole truth.
Killing Watson would have hurt Sherlock but it wouldn't have been quite as much fun would it?
Plus, as we see later on, he's integral to the torture. Sherlock is forced to choose between killing his biological brother, Mycroft and his brother in adventure/life, Watson.
Mycroft: "This is family"
Sherlock: "That's why he stays!"