The leader of the small band of men who were martyred in Kerbala was none other than Hussain(pbuh, the grandson of the Holy Prophet(pbuh).
With the passing away of his brother Hassan(pbuh) in 50AH, Hussain (pbuh) became the leader of the household of the Holy Prophet(pbuh. He respected the agreement of peace signed by Hassan(pbuh) and Muawiya, and, despite the urging of his followers, he did not undertake any activity that threatened the political status quo. Rather he continued with the responsibility of looking after the religious needs of the people and was recognised for his knowledge, piety and generosity. An example of the depth of his perception can be seen in his beautiful du'a (supplication) on the day of Arafat, wherein he begins by explaining the qualities of Allah, saying:
" (Oh Allah) How could an argument be given about Your Existence by a being whose total and complete existence is in need of you? When did you ever disappear so that you might need an evidence and logic to lead (the people)towards You? And when did You ever become away and distant so that your signs and effects made the people get in touch with you? Blind be the eye which does not see You (whereas) You are observing him. What did the one who missed You find? And what does the one who finds You lack? Certainly, the one who got pleased and inclined toward other than You, came to nothingness (failed)."
On the other hand, we have Yazid, whose father (Muawiya) and grandfather had always tried to sabotage the mission of the Holy Prophet, and who showed his true colour by stating in a poem, "Bani Hashim had staged a play to obtain kingdom, there was neither any news from God nor any revelation.
Yazid was a pleasure-seeking person, given to wine drinking and playing with pets. It is no wonder that Husain's response to Yazid's governor, when asked to pay allegiance to Yazid was, "We are the household of the prophethood, the source of messengership, the descending-place of the angels, through us Allah had began (showering His favours) and with us He has perfected (His favours), whereas Yazid is a sinful person, a drunkard, the killer of innocent people and one who openly indulges in sinful acts. A person like me can never pledge allegiance to a person like him. The revolution of Hussain (pbuh) was an Islamic movement spearheaded by one of the great leaders of Islam. The principles and laws of Islam demanded that Hussain(pbuh) act to warn the Ummah of the evil situation which it was in, and to stand in the way of the deviating ruler. As Hussain(pbuh) himself remarked when he left Madina for the last time, "I am not rising (against Yazid) as an insolent or an arrogant person, or a mischief-monger or tyrant. I have risen (against Yazid) as I seek to reform the Ummah of my grandfather. I wish to bid the good and forbid the evil.
For further reading or getting info, you could look at the following link: http://www.shianews.com/hi/articles/islam/0000351.php
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