Is the man considered the head of the family even if he is not the primary source of income in it?

Guardianship (Qawamah) is a right that Allah has specifically granted to men over women, so that men may take charge of their affairs, guide them, and oversee them. Allah Almighty says: "Men are in charge of women by [right of] what Allah has favored some of them over others and by [right of] what they spend from their wealth." Among the reasons for this guardianship are: the completeness of a man's intellect and discernment, his completeness in religion due to the absence of periods of interruption in his worship, and his expenditure of wealth, such as the dowry and maintenance. This guardianship does not fall away from the man if the woman spends on him; rather, that would be considered an act of kindness on her part.