How can the two Hadiths be reconciled: Imam Al-Bukhari's Hadith about the Prophet (peace be upon him) drinking milk on the Day of Arafat while he was not fasting, and Imam Muslim's Hadith about the virtue of fasting on the Day of Arafat and that it expiates for two years?

It has not been reported that 'Aishah gave the Prophet, may Allah bless him and grant him peace, a cup of milk on the Day of 'Arafah while he was not performing Hajj. What is authentically reported in the Two Sahihs is that Umm Al-Fadl sent a cup of milk to the Prophet, may Allah bless him and grant him peace, while he was in 'Arafah, and he drank it. This does not contradict the desirability of fasting on 'Arafah, because fasting is desirable, not obligatory.