Why Observing the Event of Ashura?

In The Name Of Allah, the Most Compassionate, the Merciful.
O Allah! Send your blessings to the head of your Messengers and the Last of your Prophets Muhammad (S.A.W.), and his pure and cleansed progeny.

Introduction
The commemoration of Imam Hussain's (A.S.) martyrdom has been observed by the followers of Ahlul Bayt (members of the House of the Prophet (S.A.W.)) for centuries; yet many Muslims resent it, thinking that it increases the division of the Muslims. To my understanding, this argument is unfounded for the following reasons:
• Imam Hussain (A.S.) and his opponent Yazeed are on the opposite ends of the Heavenly Scale. There is no Muslim School that doubts the purity and qualification of the Imam (A.S.). Righteous Muslims also know that Imam Hussain is a dear grandson of the Prophet Muhammad (S.A.W.), and that he is a leader of the youth of the paradise. On the other hand, Yazeed is un-acceptable to any Muslim, and every Muslim condemns him, and will continue to do so, for his transgression and for the crimes he committed against the Ahl al Bayt. With such a clear distinction, there should be no confusion among the Muslims because of the commemoration of this great Imam. No Muslim party should be angered by hearing the truth about the great Imam and his opponent Yazeed!
• Imam Hussain (A.S.) and the rest of the Ahl al Bayt did not receive in their lives the fairness and respect due to them on the part of the Muslims, while the rest of the Companions of the Prophet ( saw ) received of that as much as they deserved ( or more ). The members of the House of the Messenger were denied even the right to live or feel safe. The Muslims, should therefore try to correct the mistake of history by un-covering the virtues of these distinguished people.
• To keep the names of these people alive is in the interest of the Muslims. The Messenger of God, Mohammad ( saw ), said when he was returning from his valedictory pilgrimage, while at Ghadir Khum: I am about to be called ( by the Lord to depart from this World) and respond (to His call). I am leaving for You the Two Valuables (one of them is bigger than the other) : The Book of God and the members of my House. Beware how you shall treat the two after me, because they will not part with each other until they join me on the Day of Judgement!

Ref:
• Mustadrak of al Hakim, vol 3 p 109
• Sahih of Tirmizi, vol 2 p 307
• Musnad of Ahmed Hanbal, vol 3 p 14, 217
• Khasais of al Nasai, p 30
• Sahih of Muslim, vol 4 p 1286 hadith 5920
• ... and many many more
Thus honoring their memories and informing people about them would be in accord with the advice of the Messenger (S.A.W.), and would provide the Muslims with what they need of Guidance.
The History of this great Martyr is a school for the seekers of the truth. Every Muslim can learn a great deal from the supreme sacrifice and the courage of the Imam. The Muslims are still living under similar conditions now as before. Corruption is still prevalent in our society, and tyrants, like Yazeed, are no rarity in Muslims and non-Muslim countries, but we do not have men like Imam Hussain. Fortunately, this commemoration is providing the Muslim World with some of his excellent students.

Ref:
Imam Hussain - Leader of Martyrs
The Late Muhammad Jawad Chirri