Anas Bin Malik (may Allah be pleased with him) narrated:

"Allah's Messenger (peace be upon him) would not leave (his house) on the day of Fir until he ate some dates."

Imam al-Muhallab said:

"The wisdom in eating before the prayer is to circumvent the assumption that one must continue to fast until the Eid prayer is over."

And Buraydah Bin al-Hasib (may Allah be pleased with him) narrated:

"The Prophet (peace be upon him) would not leave (his house) on the day of Fir until he ate. On the day of Nahr (slaughtering) he would not eat until he returned - so that he would eat from his sacrifice."

The great scholar ash-Shawkani said:

"The wisdom in delaying eating on the day of Adha (sacrifice) is that it is a day on which it is legislated to offer sacrifices and to eat from them. Thus, it is recommended for one to eat from his sacrifice on breakfast. This was mentioned by Ibn Qudamah."

Az-Zayn Bin al-Munayyir said:

"The time that the Prophet (peace be upon him) ate his breakfast on each of the two Eids occurred at the proper time of giving out their related sadaqah (charity), thus dispensing of the Fitr charity before going to the musalla, and dispensing of the sacrifice's charity after slaughtering it."

It must be noted here that, nowadays, people no longer slaughter their sacrifices at the musalla. They do that at distant places, and sometimes do not get the meat until the evening or the following days. In this case, it is understandable that the sunnah of eating breakfast from the sacrifice's meat cannot be reasonably fulfilled.