Fasting the day of Ashura is called by our Imams as (The Fast of Ibn Marjana) according to the narrations. Ibn Marjana was the commander of the army of Yazeed who killed Imam Husain (AS).
It is Makrouh (Disliked) to fast that day. Ibn Marjana and his people wanted to celebrate the day of Ashura to make Muslims forget their crime, that it why they paid lot of money to false narrators to fabricate narrations encouraging people to fast and celebrate that day. We have evidence that narrations encouraging fasting on the day of Ashura are fabricated by enemies of Ahlul Bayt (AS).
The recommended on the day of Ashura is to remember the tragedy of Karbala and weep and cry on it and refrain from eating and drinking till after noon. This is called Faqa.