A woman does not have to get permission from her husband for every little task, but it would be better to consider the customs of the community in these issues in order to avoid problems.
About the cooking issue,
Let us say firstly that not everything in life is about halaal and haraam. But everything in life has measures. Allah the Almighty commands:
“We have created everything in a determined measure.” (54:49)
There are many verses in Quran that give us some information about that “determined measure” of husband-wife relations.
According to Quran, husbands are responsible, therefore authorized for the issues regarding the safety and economic welfare of the family (4:34); husbands and wives (should) have an equal-weight of responsibilities in the family (2:228); married couples are expected to live in acceptable terms (4:19); men have a right to marry up to four women, therefore are allowed to divide their time and effort on housework and the children to %25 without losing their authorities over them while women cannot (4:3); women are responsible for suckling their children (2:233) and advised to stay in their homes as a sign of dignity (33:33), etc.
If all of these evidences are to be read and evaluated together, one can see that:
In a natural family, leaving aside the exceptions and exceptional lifestyles,
– Men should first be earning money, spending their time, money and effort on the safety and well-being of their families.
– Women should be first raising the children, taking care of the basic housework and helping their husbands.
There’s no obstacle for going beyond these duties, like men helping their wives in housework and/or women working to earn more money for the well-being of their family. There’s no obstacle, no prohibition. But we always see, experience big problems and divorces in the families where these primary, natural duties are disregarded.
It is not obligatory (fard) for you to cook the meal, but you should do it.
Because it is a natural duty and it is expected from you.
What will you do to balance the scales of responsibility if you don’t cook, and will it please your husband more?
If one party undertakes more responsibility than the other, it will certainly cause problems and it will be you to suffer the consequences. Marriage is just another form of the many tests in this temporary life. Being patient and dutiful is the key to win.