Kardama Muni was anxious about his good wife, Devahuti, while leaving home, and so the worthy son promised that not only would Kardama Muni be freed from the material entanglement, but Devahuti would also be freed by receiving instruction from her son. A very good example is set here: the husband goes away, taking the sannyasa order for self-realization, but his representative, the son, who is equally educated, remains at home to deliver the mother. A sannyasi is not supposed to take his wife with him. At the vanaprastha stage of retired life, or the stage midway between householder life and renounced life, one may keep his wife as an assistant without sex relations, but in the sannyasa order of life one cannot keep his wife with him. Otherwise, a person like Kardama Muni could have kept his wife with him, and there would have been no hindrance to his prosecution of self-realization.
Kardama Muni followed the Vedic injunction that no one in sannyasa life can have any kind of relationship with women. But what is the position of a woman who is left by her husband? She is entrusted to the son, and the son promises that he will deliver his mother from entanglement. A woman is not supposed to take sannyasa. So-called spiritual societies concocted in modern times give sannyasa even to women, although there is no sanction in the Vedic literature for a woman’s accepting sannyasa. Otherwise, if it were sanctioned, Kardama Muni could have taken his wife and given her sannyasa. The woman must remain at home. She has only three stages of life: dependency on the father in childhood, dependency on the husband in youth and, in old age, dependency on the grown-up son, such as Kapila. In old age the progress of woman depends on the grown-up son. The ideal son, Kapila Muni, is assuring His father of the deliverance of His mother so that His father may go peacefully without anxiety for his good wife.
Source: A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Third Canto, Chapter 24 – Text 40