Abu Huraira (Allah be pleased with him) reported that the Messenger of Allah (ﷺ) forbade fasting on these two days. 'Id-ul-Adha and 'Id-ul-Fitr.
Sahih Muslim Book 13, Hadith 178
← Previous Hadith I observed Id along with Umar b. al-Khattab (Allah be pleased with him). He came (out in an open space) and prayed and (after) completing it addressed the people and said: The Messenger of Allah (ﷺ) has forbidden the observing of fast on these two days. One is the day of Fitr (at the end of your fasts), and the second one, the day when you eat (the meat) of your sacrifices.

Sahih Muslim Book 13, Hadith 177 Next Hadith → I heard from him (Abu Sa'id) a hadith which impressed me, and I said to him: Did you hear it from the Messenger of Allah (ﷺ)? Thereupon he said: (Is it possible) that (I should) say about the Messenger of Allah (ﷺ) that which I have not heard? I heard him saying: It is not proper to fast on two days, Adha and Fitr (at the end) of Ramadan.

Sahih Muslim Book 13, Hadith 179