Question: Is it true that according to Islam a wife needs her husbands permission to leave the home? To what extent is this obligatory? Why should a wife always show obedience to her husband? Please explain in detail.
    Answer: In Islam, for the welfare and harmony of the family set up, Islam requires that the wife adopt an attitude of adjustment and harmony with the husband and the husband is required to be affectionate and accommodating as far as possible to the needs of his wife. He must not impose any undue restrictions on her for this will ignite the wrath of God upon him. 
    With regard to a wife seeking her husband’s permission before leaving the house, the proper perspective must be understood. In general circumstances of mutual trust, there is no need for a wife to ask permission from her husband to go out. However, in certain circumstances in which the husband genuinely considers that going out might disrupt the family in any way, he has the authority to exercise his right of stopping her and in these circumstances, she should always ask permission to leave the house. In this regard, the husband must remember that if he imposes himself without any sound and justifiable reason, he would be crossing the bounds and invoking the displeasure of the Almighty. His wrong behavior may even lead the wife to abandon him for which he would be solely responsible if he adopts an unreasonable attitude. 
    As far as the second part of your question is concerned, the concept of a wife being obedient to her husband and showing submission to him must be understood in the proper perspective. A family by analogy is similar to a state. All citizens of a state are expected to abide by the rules and regulations of the country they live in. They are expected to adopt an attitude of adjustment and harmony with the country. This, of course, does not mean that they cannot differ with its policies. They have the inalienable democratic right to differ and present their differences in a befitting manner. This submission is actually an essential requirement for discipline and order without which anarchy may result. Similarly, in the case of a family set up, it is essential that the person who is its head be shown obedience. In other words, submission to authority is not specific to the gender of the authority. Whoever is the authority, must be submitted to. Gender does not dictate submissiveness -- it is authority which does. It is common knowledge that in different sphere of activities people have different abilities and justice entails that a person be made responsible according to his or her abilities and given authority on that basis. We have been informed by divine revelation that it is the husband who is more suitable to be the head of the family. Owing to this relative superiority, women are directed to submit to men not because men are superior human beings, but because in this particular case it is the men who have been vested with authority in accordance with the following verse: 

Men are the guardians of women because Allah has given one superiority over the other and because they [-- men --] support them from their means. (4:34) 

    If women had been more suitable for the task of heading a family, men would have been similarly directed to adopt this attitude of adjustment.