Wa`alaykum As-salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister in Islam, thanks for this interesting question. We really commend your efforts in pursuit of truth. This is what is required of all people, to seek truth and not to give in to anything that may cloud their minds with false ideas about Islam.
First of all, it should be clear that a woman is equal to a man in the pursuit of education and knowledge. When Islam enjoins the seeking of knowledge upon Muslims, it makes no distinction between men and women. Almost fourteen centuries ago, Prophet Muhammad (peace and blessings be upon him) declared that the pursuit of knowledge is incumbent on every Muslim, male and female. This declaration was very clear and was implemented by Muslims throughout history.
Focusing more on the question you posed, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Every Muslim, whether male or female, is obligated in Islam to seek at least the basic education in religion.
The Prophet (peace and blessings be upon him) said, “Seeking knowledge is a duty of every Muslim.” If women had been excluded from this exhortation, the Prophet (peace and blessings be upon him) would have certainly said so. In fact, in another version of the same hadith, it is said, “…on every Muslim, male and female”. Allah tells us in the Qur’an: (Ask those who know, if you have no knowledge.) (An-Nahl 16: 43)
Based on many such proofs in the Qur’an and Sunnah, Muslim scholars have ruled that seeking essential knowledge of the beliefs and practices of Islam is an obligatory duty of every Muslim, regardless of gender.
It is common knowledge that as Muslims we must practice Islam in order to gain salvation. Scholars tell us that our practice of religion is not valid or acceptable unless it is based on sound knowledge. It follows from this that seeking knowledge about the essentials of religion is an obligation on both males and females.
Religious education aside, Muslim women must also strive to acquire essential life-skills that would make them self-reliant. If we take into account the volatile nature of social circumstances in this daytime and age, it would be suicidal for Muslim women to ignore such training; Allah warns us against dragging ourselves into perdition.
Still another factor to consider: In Islam, women’s roles in rearing future generations of Muslims are far more crucial than that of men. It goes without saying that we cannot rear intellectually and physically healthy children unless mothers are educated and can, therefore, educate children. Based on this fact, it is not at all amazing when we see that all of the great scholars of Islam had educated mothers who planted the first intellectual seeds of greatness in their lives.
Quoted, with slight modifications, from: www.islam.ca