In fact, the status of woman in Islam constitutes no problem. The attitude of the Qur'an and the early Muslims bear witness to the fact that woman is as vital to life as man himself, and that she is not inferior to him nor is she one of the lower species. Had it not been for the impact of foreign cultures and alien influences, this question would have never arisen among the Muslims. The status of woman was taken for granted to be equal to that of man. It was, of course, a matter of fact, and no one then considered it as a problem at all.
As for the `ibadat (acts of worship), we have to carry out them in the same and exact way prescribed by Allah Almighty and taught by the Prophet (peace and blessings be upon him). There are some slight differences in carrying out some acts of worship between men and women, in a way that best suits their different natures. For example, in Hajj women are allowed to wear their normal clothes or attire regardless of whether they are with seams or not, while men are not allowed wear clothes with seams. This is, of course, in favor of women's nature and need to cover their entire body with the exception of the face and hands.
Focusing more on the question at hand, Dr. Muzammil H. Siddiqi, former president of the Islamic Society of North America, states:
Islam places no restriction on women to teach, preach, and guide both women and men. There are many women today who are fully qualified to be jurists (faqihah) and give religious opinions (fatwas). Leading salah (prayer), however, is restricted to male imams only when the congregation consists of men and women, whether the prayer is performed in the mosques or outside mosques, whether they are daily prayers or Friday and Eid prayers. Women are not allowed to lead such prayers.
This has also been the practice of Muslims all over the world since the time of the Prophet (peace and blessings be upon him). This sharia ruling is not because of any notion of spiritual deficiency among women. Men and women both are equal in the sight of Allah and both of them must be fully respected and honored. Women are allowed to lead the prayer when the congregation is all women. They are also allowed to lead the prayer in their homes among their family members, if they are more knowledgeable of the Quran and Islamic rules.