Re: Fasting on Ashura ..
Peace All,
I won’t go in full details but i’ll quote some main points. You may well research on that and correct me if i’m wrong. 
The hadith regarding fasting on the day of ‘Ashura’ were narrated from Umar, Ar Rubi bin Muawdah, Salim’s father, Humaid bin Abdur Rahman, Aisha, Abdulla b. Umar, Qais b. Sakan, Ibn Masudd, Alqama narrated from Ashath b. Qais, Jabir B Samura, Muawiya b. Abu Sufyan, Abd Al-Rahman, Ibn Bishr, Abu Musa, Hakam b. Araj, Ibn Abbas, Salama b. Al-akwa, Rubayyi b. Muawwidah b. Afra, Khalid b. Dhakwan, Abu Qatada and many many more. Foremost Prophet Muhammad
observed fast on this day i.e., on Ashura by Himself
let alone all narration if anyone doubtful from the narrations or narrators. He
did and one who observe fast on this day will be rewarded by Almighty Allah and in case if don’t than there is no sin or harm on him/her. Prophet
also said one who wish to fast he/she may fast and if don’t then donot fast. Basically its optional and its matter only to gain more rewards.
Some said in past Jews were observe fast on Ashura day as ‘this is a good day’ for them. Due to that tradition or in comparison, Muslim also observing the fast on this day. According to some scholars the jews were saved from pharaoh and ‘Hazrat Moosa a.s., fasted on this day as ‘in gratitude to Allah’, so that is why Muslims fast on this day’. In other words we can say we fast it our of respect for it’. If Prophet
told the peoples to fast b’coz we are more closer to Moosa a.s. than my understanding it that this is b’coz we all creed are from one and same God.
Another reason of observing the fast on the day of Ashura is for expiation of minor sins. Also it is written that on this day i.e. Ashura, Kaaba was covered.
Lastly, in the Holy book of Qur’an, Almighty Allah said that there are four months which are more sacred. Prophet Muhammad
observed fast in these months for more reward as well as for expiation of forgivness of sins. So anyone can observe fast as supererogatory seeking more rewards and/or for forgivness of sins in these month.
I don’t see there is any issue either we fast on this day i.e., day of Ashura or not. It is matter for seeking more rewards and come a step closer to Almighty Allah.
Almighty Allah knows best.