Bukhari

Hadith Commentary:
(1)
From these ahadith, it is understood that fasting on the days of Eid al-Fitr and Eid al-Adha is prohibited, whether the fast is due to a vow (nazr), expiation (kaffarah), voluntary (nafl), or a make-up (qada) fast; in short, fasting of every kind is prohibited on these days.
There is no disagreement about this.
In fact, Imam Bukhari rahimahullah, through this heading, has pointed towards a particular difference of opinion: if someone makes a vow to fast on a specific day, and by coincidence that vow falls on the day of Eid. For example:
Someone says, “On the day Zaid arrives, I will fast.”
If Zaid arrives on the day of Eid, will the vow be valid or not? According to the majority (jumhur), such a vow is not valid because fasting on that day is prohibited. However, according to the Hanafis, the vow will be valid, but the person will be required to make up (qada) the fast on another day.
In any case, the vow for that day is not valid because the Messenger of Allah sallallahu alayhi wa sallam has prohibited fasting on that day.
(Fath al-Bari: 4/304) (2)
In the mentioned hadith, there is an indication towards the reason due to which fasting on these two days is prohibited.
One reason is that, due to the breaking of the fast (iftar), fasting on this day is prohibited, because fasting and breaking the fast are opposites and cannot be combined at the same time. Similarly, on the day of eating the meat of sacrifice (udhiyah), fasting is also prohibited, because the requirement to eat the sacrificial meat necessitates that one should not fast on that day.
(3)
Besides these two days, fasting on the days of Tashreeq (the 11th, 12th, and 13th of Dhu al-Hijjah) is also prohibited. However, a pilgrim performing Hajj al-Tamattu‘ who does not have an animal for sacrifice may fast on these days.