Sahih Muslim

Kitab al-Sawm (Fasting), hadith no. 2518
Ibn Abbas relates that the Messenger of Allah found the Jews of Madinah fasting on the day of Ashura. The Messenger of Allah came to them and said, “What fast is this of yours?” The Jews answered, “We give thanks to Allah, for on this day (Ashura) Allah saved Musa from Pharaoh’s pursuit.” The Messenger of Allah said, “I have a better claim to Musa than you.”

Hadith no. 2528
Ibn Abbas relates that the companions said to him, “O Messenger of Allah, Ashura is a day held in high regard by Christians and Jews.” The Messenger of Allah then said, “Next year, insha Allah, we shall fast on the day of Ashura.” But the Messenger of Allah died before the following Ashura.

Sahih Bukhari

Book of Fasting, hadith no. 117
Narrated by Aisyah: the Quraysh always fasted on the day of Ashura before Islam was revealed, and the Messenger of Allah likewise ordered the Muslims to fast on Ashura, until the fast of Ramadan was made obligatory and he said, “Whoever wishes to fast on the day of Ashura may do so, and whoever does not wish to fast is permitted not to.”

Let us examine the hadiths above critically.
1. The Messenger of Allah asked the Jews about the fast. Where was Jibril? Was Jibril resting? Why did the Messenger of Allah not ask Jibril? Why was no revelation sent down concerning fasting on the day of Ashura?
2. When the Messenger of Allah said that next year we would fast, that would be the year 9H, since the Messenger of Allah died in 10H. Yet we know that from the year 6H there was not a single Jew left in Madinah.
3. In Sahih Bukhari, Aisyah states that the Ashura fast was already observed before the time of Islam, and that the Messenger of Allah ordered the fast on the day of Ashura before the fast of Ramadan was made obligatory. This hadith contradicts outright the earlier report in Sahih Muslim, which has the Messenger of Allah only then learning of the fast on the day of Ashura.

From the criticism above we may conclude that these hadiths do not accord with the facts, and so cannot be relied upon. They even contradict one another, and their authenticity is open to question.