He is not thinking of his responsibility to her, but of his rights over her, and of her obligations towards him." This interpretation makes it sound as if the man is expecting the woman to bear him children. In a time where women were considered men's property anyway, not only would the woman be possessed by her husband, but her children as well.
This interpretation implies that he is more focused on his rights over her and her obligations towards him rather than his responsibility to her. Given the societal norms where women were considered property, she would not only be under her husband's control but also potentially his progeny.