Question: It is customary that young men go and propose to young women. It is considered ugly among people when young women go and propose to young men, whereas we find the Qur'an saying, (…and a believing woman if she gave herself to the Prophet, if the Prophet desired to marry her- specially for you, not for the (rest of) believers).(33:50) My question is: which is right – what the Muslims did at the time of the Prophet (S) or what is customary in our present age?
The answer: Customs, sometimes, control the affairs of people while people have no choice in it. The position of Islam in this concern is that the more important thing has to be preferred to the important thing while preserving the benefits of people and moving gradually towards the teachings Islam has established.
Yes! This Qur’anic verse is clear in this concern. Imam al-Baqir (a.s.) narrates that once a woman from Medina came to the Prophet (S) and said, ‘O messenger of Allah, a woman does not go to engage a husband. I have been a widow for a long time and I have no child. Do you want me (to be your wife)? I have given myself to you if you accept me…’ .
This woman came to the Prophet (S) by herself and asked him to marry her, and the Prophet (S) neither chided her nor disapproved of her doing so. This means that this matter was natural in Islam. Besides, the Qur'an has mentioned this matter without any implication of ugliness. Khadeeja (a.s.) herself asked the Prophet (S) to marry her, and she was the head lady of her time.
A proposal made by a virgin or a widow is not prohibited in the Sharia, but customs have their respected position if they do not oppose the Islamic values. In fact, in our present time, there does not have to be a contradiction between customs and the wishes of a girl when she finds a suitable husband. The potential husband can be informed secretly of the wish of the girl. If he accepts, he can go and propose to the girl according to customs; otherwise, he should bury the matter and keep the secret forever. This is a trust and a traitor will be answerable on the Day of Resurrection. In this way, as I think, the two manners can be practiced together.
 Usul al-Kafi, vol.5 p.568.