The Messenger of Allah ﷺ stated on various occasions that the days of the ʿĪd al-Fiṭr and ʿĪd al-Aḍḥā are days in which one benefits from the blessings bestowed by Allah, and he prohibited fasting on these days.
(See: al-Bukhārī, Ṣawm, 65–66; Muslim, Ṣiyām, 138–145; Abū Dāwūd, Ḍaḥāyā, 10)
Based on these narrations, the jurists have derived the ruling that it is not permissible to fast on the first day of ʿĪd al-Fiṭr and on the four days of ʿĪd al-Aḍḥā. Indeed, these days are days of divine hospitality granted by Allah to His servants. They are days of eating and drinking, of sharing the joy of the festival with fellow Muslims, and of sitting together at the table.
During such times, a Muslim does not fast but rather seeks to partake in the collective joy of the festival alongside other Muslims. For this reason, the Messenger of Allah ﷺ prohibited fasting on these days and described them as days akin to a banquet that Allah has opened for His servants.