Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If a woman does not like a man for his moral conduct or his physical appearance, it is desirable for her to be patient with this, as Allah may reconcile between the two and bring them together.
However, she can ask for a divorce, and if he refuses, then she can suggest to give him some money-in return-for the divorce. It is a Sunnah for the husband to accept the request of the wife, but he is not obliged to do so.
The evidence about this is the Hadith reported by Bukhari, that Ibn Abbas (Radiya Allahu Anhu) said: 'The wife of Thabit Ibn Qays came to the Prophet (Sallallahu Alaihi wa Sallam) and said: "O, Prophet of Allah (Sallallahu Alaihi wa Sallam), I do not blame him for his conduct or religion, but I fear to apostate from Islam (because of my uneasiness with him)." So the Prophet (Sallallahu Alaihi wa Sallam) told her: "Can you give him back the garden he offered you as a dowry in exchange for the divorce." She replied: 'Yes'. Then the Prophet (Sallallahu Alaihi wa Sallam) told Thabit, "Accept the garden and divorce her."
Therefore, if a woman asks her husband to divorce her due to not liking him , she is not sinful by doing so, especially if she fears not to fulfill his right. The order of the Prophet (Sallallahu Alaihi wa Sallam) for Thabit is an order of guidance and not an obligation.
The marriage contract is in the hands of the husband and the wife cannot break it except with the consent of the husband. So it is not sufficient for the wife to let her husband know that she has left him, or give him back what he offered her (as a dowry); except with his consent, or an Islamic authority has to give a rule about this.
Allah knows best.