It was by means of the speeches given by the captives of Karbala...
It was by means of the speeches given by the captives of Karbala, led by Imam al-Sajjad (as) and Zaynab al-Kubra, that the oppression and crimes committed by Yazid were exposed. It was because these crimes were publicly disclosed by the captives that Yazid could not achieve his sinister and ominous objectives.
Imam al-Husayn (as) knew very well that if he and all his children and companions were killed, and some of his household members were not present to witness his martyrdom, no one would disclose the oppression committed against him to the public. There had to be some family members who should remain alive and be taken into captivity so that they could disclose the oppression that was committed against him, or all the blood which would be shed would have been futile.
This is why Imam al-Husayn (as) brought the womenfolk of his household along with him and why this act was considered necessary. It can therefore be said that the public speeches which were given by the womenfolk of Imam al-Husayn’s (as) household shook the foundations of Yazid’s government and eventually brought about its collapse.
Objection This possibility, although rational, does not completely meet the needs of our question either because still a second question comes to mind: Why did Imam al-Husayn (as) bring even the newborns of his household? The duty of divulging the events of Karbala could be left to certain older members of his household, as was done by Imam al-Sajjad (as) and Zaynab al-Kubra, and the other women who were in Imam al-Husayn’s (as) caravan.
There was no need to bring the children and newborns to accomplish this duty. Therefore, this argument does not explain the entire cause for bringing all the members of his household, although it can be cited as one of the philosophies behind bringing his family along.
Third response Some people, while trying to provide a response to this question, have focused on the human tragedies of this event, and have emphasized that Imam al-Husayn (as) intended to prove and expose Yazid’s inner self and the crimes he had committed against Islam and the Prophet’s (as). That is why Imam al-Husayn (as) brought all the members of his household, including the women and children.
Even though he knew what Yazid would do to his family members, Imam al-Husayn (as) brought them along in order to prove the true nature and identity of Yazid and his government.