Why does Mollie run away from the farm?

To answer this question, take a look at Chapter Five. According to the narrator, Mollie has become increasingly troublesome. She doesn't want to do any work and would rather spend her time gazing at her own reflection in the drinking pool.
After an intervention from Clover, Mollie disappears and is later seen in the village being stroked by a human and wearing a scarlet ribbon.
The answer to why Mollie runs away, therefore, lies in her materialistic and shallow nature. Ever since the early days of the Rebellion, Mollie's only interest has been in sugar lumps and ribbons, not in freedom and equality. All she wants is to be loved and admired and, without any humans around, this will not happen.
Mollie, therefore, flees the farm and finds a new human master who will give her the affection and ribbons she so deeply desires and which are prohibited on the farm by the principles of Animalism.