Without the allegiance of the strongest existent forces...
Without the allegiance of the strongest existent forces, a government would not stay in power for long. To withhold one's allegiance was considered to be a crime and brought disgrace and dishonour. Following the example of the Prophet, people believed that allegiance, when given by free will and not through force, carried authority and weight. Mu'awiyyah had realized that putting pressure upon the Imam would only to serve to push an acceptable situation to the breaking point.
Yazid did not pay heed to the last will of his father which was not to force the allegiance of Imam Husayn ('a). Rather, he immediately began pushing for the oath of allegiance. Imam Husayn ('a) fled to Mecca and sought refuge within the Ka'ba. He remained in that city for four months and during that time he received letters and pledges from the entire Islamic world asking for his help in overthrowing the oppressive Ummayyid rule.
In particular, he was invited by the people of Kufa to come and live among them and rule them. So we find Imam Husayn ('a) not able to turn back to Medina for he would, by so doing, sanction a government of injustice and tyranny. He would be expressing public contempt of Islam. He could not betray Islam by such an act even though he knew it meant certain death for him. To go forward to Kufa also had its dangers for the people were not completely trustworthy. He decided to go forward.
Through this decision, he sealed his fate. The journey he undertook towards Kufa was a journey towards the place where his father, Hazrat Ali had been killed 20 years earlier. He sent his cousin, Muslim ibn 'Aqil, to Kufa to see what the situation was like. Ibn Muslim was at first successful in receiving many pledges from the people of Kufa. He sent the pledges and good tidings of the people of Kufa to Imam Husayn ('a).
Once Imam Husayn ('a) received the pledges and news from Ibn Muslim, he, his companions and his family began the journey towards Kufa. Meanwhile, Yazid heard of the work of Ibn Muslim and was most disturbed. He sent orders to his son to put a stop to the activities of Imam Husayn ('a)'s emissary. Ibn Muslim was then murdered by Yazid's son, Ibn Zayd. Only a few days journey from Kufa, Imam Husayn ('a) learned of the murder of Muslim and his sons.
In spite of this news and other warnings which he had received, Imam Husayn ('a) refused to turn back and instead, continued moving towards Kufa.