The literalist school (Ahl al-Ẓāhir) categorically prohibited fasting on those days, while another group permitted it without reservation, and yet another—among them Imām Mālik—considered it disliked. Mālik, however, made an exception for the pilgrim who is required to fast during the Hajj, namely the tamattuʿ pilgrim.
Those days are the three days that follow the Day of Sacrifice (the Days of Tashrīq).
The source of their disagreement lies in how they understand the Prophet’s statement, peace and blessings be upon him, that these are “days of eating and drinking.” If the words are taken as an obligation, fasting is unlawful; if taken as recommendation, fasting is merely discouraged. It seems that those who viewed it as recommendation only preferred that interpretation over the more obvious one—namely, obligation—because they observed that interpreting it as obligatory would conflict with the authentic report of Abū Saʿīd al-Khudrī, derived by implication, in which he said:
“I heard the Messenger of Allah—may Allah bless him and grant him peace—say: ‘Fasting is not valid on two days: the Day of Fitr at the end of Ramadan and the Day of Sacrifice.’”
By implication, this ḥadīth indicates that fasting on any day other than those two is valid; otherwise, restricting the prohibition to them would serve no purpose.
As for Friday, some scholars—among them Mālik, his companions, and a number of others—saw no dislike in fasting it, whereas another group considered it disliked unless one also fasted the day before or the day after.
The reason for their divergence is the conflicting narrations on the matter:
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The ḥadīth of Ibn Masʿūd, authentically transmitted: the Prophet—peace and blessings be upon him—“used to fast three days of every month, and I never saw him break his fast on a Friday.”
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The ḥadīth of Jābir, recorded by Muslim: when someone asked him, “Did you hear the Messenger of Allah—peace and blessings be upon him—forbid singling out Friday for fasting?” he replied, “Yes, by the Lord of this House!”
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The ḥadīth of Abū Hurayrah, also in Muslim: the Messenger of Allah—peace and blessings be upon him—said, “None of you should fast on Friday unless he fasts a day before it or a day after it.”
Those who follow the outward sense of Ibn Masʿūd’s report allow fasting on Friday without restriction. Those who adhere to the outward sense of Jābir’s report deem it disliked in every case. Those who rely on Abū Hurayrah’s report reconcile the two earlier reports—namely, those of Jābir and Ibn Masʿūd.