His father, Ali (the fourth caliph), was assassinated and when the Muawiya/Yazid took over, there was already a faction forming within the Muslims that believed the caliphate was stolen (Shia is actually short for Shiat Ali, The Ali party). But killing Hussein and his small army in Karbala when he opposed them, and further mutilating their bodies on the field, and then killing the rest of prophet’s own blood by the Sunnis is what put the cap on the formation of the Shia sect.Husayn Ibn Ali was not a shia nor were his family. Majority of the victims of the Umayyads were Sunnis.
The Umayyads were power hungry absolute monarchy and killed any who posed a threat. Husayn Ibn Ali ra knew very well what he was doing when he left for Kufa. He fought and died for what he believed in, so did Abdallah ibn Zubayr