The practice of fasting on 10th Muharram (Ashura) in the Sunni culture has nothing to do with the tragic results of the battle of Karbala. Instead, it involves a very different story, constructed years after the Prophet's (S) death with a specific motive. The Prophet (S) never observed fast on the 10th of Muharram. It started through one of the unauthentic ahadith written and compiled by Imam al-Bukhari that says:
Prophet Muhammad (pbuh) entered Medina in the first year of Hijra and noticed the Jews fasting. He asked one of his companions: “Why are the Jews fasting?”. His companion replied: “The Jews are remembering when Prophet Moses (pbuh) and the children of Israel were saved from the Pharaoh”. The prophet said: “I have a greater right on Moses than what they do. Therefore, my people will fast on Ashura in the same way they are fasting on Ashura”. One of the companions exclaimed: “O Messenger of Allah, but we are going to be copying the Jews” and the prophet then replied: “You are right, from now on we will fast on the 9th and 10th”. (Al-Bukhari, hadith 1865)
The above hadith claims that the Jews observed this month as sacred and also observed fast during the 10th of Muharram as it coincided with their religious event of Passover. Further it claims that when the Prophet heard of the Jews fasting on 10th Muharram (the Jews were supposed to have said that Moses observed fast on 10th Muharram), the Prophet allegedly also decided to fast.
A careful analysis of historical data with all its facts exposes the manipulation of Bukhari Hadith No.1865 that's responsible for starting the practice of fasting on 10th Muharram. The Jews didn't fast on the 10th of Muharram as Passover never coincided with Muharram. The Jews had their own calendar. They had no reason to fast on the 10th of Muharram - unless it could be proven that this date coincided with some Jewish day of fast during the Medinah period in Islamic history. But there's no evidence of that either.
In accordance with historical findings, during the very ancient days, the Jewish month of Tishri coincided with Muharram once upon a time. But history bluntly indicates that the Arab and Jewish calenders lost their synchronization and parity long before the Prophet (S) migrated to Medinah in 622 CE. The parity was lost before the advent of Islam as the pagan Arabs did not follow any mathematical calculation in their intercalation. That's the reason why Muharram in the second year of Hijrah began on July 5, 623 C.E. (Al-Munjid, 21st ed.), much before the Jewish month of Tishri I (which always coincides with September-October). It was for this reason that neither the Jews nor the Arabs ever discussed anything about the synchronization of their calenders during the Prophet's entire era in Medinah. The day of Ashura had NO significance for the Jews.
Furthermore, according to the Jewish Bible, the month in which the Israelites were freed from the tyranny of Pharaoh was Abib (in Hebrew, which is the same as Rajab in Arabic). The Jewish Bible (Torah) says: "Observe the month of Abib, and keep the passover unto the Lord thy God: for in the month of Abib the Lord thy God brought thee forth out of Egypt by night." (Deut., 16:1). As the Jewish Bible mentions that Passover took place in the month of Abib (or Rajab), how could the Jews transfer that event from Rajab to Muharram in open defiance to their religious scripture? The narrator of this forged hadith obviously overlooked this point. This narrator only knew that once upon a time Muharram coincided with the Jewish month, Tishri, but he was totally unaware of contemporary rules of Jewish religion and culture.
Most importantly, something for Sunni Muslims to reflect upon which they unfortunately ignore for the purpose of defending the contents of this very unauthentic Hadith.
The Prophet (S) was sent by Allah Almighty with a perfected Religion to abrogate all previous religions that were changed and corrupted by the selfish desires of the human mind. Thus, would the Prophet (S) ever decide or agree to imitate the custom of the Jews and order people to fast on that day when the Noble Quran commands to fast ONLY in the month of Ramadan? He would NEVER do that for certain.
Syed Saeed Rizvi who has widely researched this issue is of the view that this story was constructed by the Ommayad rulers in collaboration with their political cronies, after the martyrdom of Imam Hussain. It was done for the purpose of portraying the day of Ashura (10th Muharram) as a day of rejoicing to distract the society from the tragic events of the incident in Karbala. Regardless of the long-standing Shiia-Sunni wrangling, it isn't hard to discern that Rizvi's well studied views make plenty of sense. It's a well-known fact that Abu Huraira, who barely knew the Prophet (S), and yet had narrated more ahadith than anyone else, was a close friend of Muawia bin Abu Sufyan, the first Ommayad caliph. It's also an open secret that Abu Huraira constructed tons of forged narrations in the Prophet's name from Muwaia's luxurious palace which he visited regularly. There were others like him too. Their loyalty toward Faith was questionable. Their obvious goal was personal benefit by befriending powerful and influential persons.
The above quoted Hadith on fasting on 10th Muharram is of the same genre as various other forged narrations by the camp followers of the Ommayads which say that it was on the 10th of Muharram that Noah's ark rested on Mount Arafat, the fire became cool for Abraham, and Jesus ascended to the heaven. In the same category came the traditions exhorting the Muslims to treat Ashura as a festive and joyous occasion.
Apart from the Hadith written by Imam Bukhari, and a few other copy-cat versions penned by Muslim bin Hajaj and Imam Tirmizi, there is absolutely no mention (let alone any evidence) in Islamic history that the Prophet (S) nor anyone else observed fast on 10th Muharram.
Indeed, one is perfectly entitled to observe optional fasts on Ashura or during the month of Muharram as a gesture of love and profound respect toward this enormous tragedy. But so-called traditionalism has introduced this practice on mythical grounds with corrupt intent, to turn the day of Ashura into a day of rejoicing.
With the commencement of the month of Muharram there are lengthy sermons in our Sunni masjids that babble and babble on this ridiculously false hadith, but not a word on the real incident of Muharram 10, 61 A.H. which is one of the most important episodes of our history with far-reaching consequences.
Briefly and simply put, this hadith is politically motivated. The Jews didn't fast on the 10th of Muharram and the Prophet (S) never observed fast on this day either. The month of Muharram and particularly the 10th of Muharram became significant in history after the martyrdom of Imam Hussain, the grandson of the Prophet, which happened in the year 61 AH (or 680 CE), years after the passing away of the Prophet (S). The Ommayad rulers were eager to downplay the relevance of 10th Muharram as Imam Hussain's martyrdom happened during the period of the second Ommayad ruler, Yazid bin Muawia.