Several reasons have been given for his not fasting at ‘Arafah:
One is that not fasting gave him greater strength for supplication.
Another is that not fasting while travelling is preferable even when the fast is obligatory, so how much more so when it is voluntary.
Another is that the day fell on a Friday, and he had forbidden singling out Friday for fasting. He therefore wanted people to see that he was not fasting that day, reinforcing his prohibition against singling it out for fasting, even if one were fasting because it was the Day of ‘Arafah rather than because it was Friday.
Our teacher, may Allah be pleased with him, took a different approach (1): it is a festival day for those at ‘Arafah because they gather there, just as people gather on a festival day. This gathering is particular to those at ‘Arafah, not people elsewhere. He said: The Prophet, may Allah bless him and grant him peace, indicated this in the hadith related from him by the compilers of the Sunan collections (2): “The Day of ‘Arafah, the Day of Sacrifice, and the days of Minā are our festival, we people of Islam.” It is clear that it is a festival for those attending that gathering because they come together on that day. Allah knows best.
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It is reported that he, may Allah bless him and grant him peace, frequently fasted on Saturdays and Sundays, intending thereby to differ from the Jews and Christians, as related in the Musnad and Sunan al-Nasā’ī (3), on the authority of Kurayb