Abu Bakr ﷺ sent me among those who were to make a public announcement on the Day of Sacrifice at Mina, "No polytheist is to perform Hajj this year, and no one is to circumambulate the House while naked. The day of the greatest Hajj is the Day of Sacrifice." It was called "the greatest" only because people used to speak of "the lesser Hajj." So Abu Bakr proclaimed this to the people that year, and in the year of the Farewell Hajj, in which the Prophet ﷺ performed the pilgrimage, no polytheist performed Hajj.
بعثني أبو بكر ﷺ فيمن يؤذن يوم النحر بمنى: لا يحج العام مشرك، ولا يطوف بالبيت عريان. ويوم الحج الأكبر يوم النحر. وإنما قيل الأكبر من أجل قول الناس: الحج الأصغر، فنبذ أبو بكر إلى الناس في ذلك العام، فلم يحج عام حجة الوداع الذي حج فيه النبي ﷺ مشرك.
Bukhari narrated it in the chapter on jizya (3177), from Abu Yaman, who said, Shuayb informed us, from Zuhri, who said, Humayd bin Abdul-Rahman informed us, that Abu Hurairah said (then he mentioned it). The Sahihayn narrated it, Bukhari in the tafsir chapter (4657) and Muslim in the Hajj chapter (1347), through two other routes from Ibn Shihab Zuhri. In it, Humayd bin Abdul-Rahman explicitly states, "The Day of Sacrifice is the Day of the Greater Hajj," on the basis of the hadith of Abu Hurairah. This suggests that the statement "the Day of Sacrifice is the Day of the Greater Hajj" is an insertion from the words of Humayd bin Abdul-Rahman.However, Abu Dawud narrated it (1946) through the route of Shuayb with his chain, adding at the end, "And the Day of the Greater Hajj is the Day of Sacrifice, and the Greater is the Hajj," which suggests that it is attributed directly to the Prophet. The correct view is that it is an insertion, as is clear in the Sahihayn from the explicit statement of Humayd bin Abdul-Rahman. This is also the view favored by Ibn Hajar in his Fath al-Bari (8/321), where he said, "His statement, 'And the Day of the Greater Hajj is the Day of Sacrifice,' is the statement of Humayd bin Abdul-Rahman, which he deduced from the words of Allah Almighty, "And a declaration from Allah and His Messenger to the people on the day of the greater Hajj" [Tawbah 9:3], and from Abu Hurairah's public proclamation of this by order of Abu Bakr on the Day of Sacrifice, which indicates that what is meant by the Day of the Greater Hajj is the Day of Sacrifice." End of quote.This hadith is among those Tahawi mentioned in Mushkil Athar, as Ibn Hajar stated in Fath al-Bari (8/318), where he said, Tahawi said, "This is problematic, because the reports concerning this incident indicate that the Prophet ﷺ sent Abu Bakr for that purpose, then sent Ali after him and commanded him to make the proclamation. So how could Abu Bakr have sent Abu Hurairah and those with him to make the proclamation, when the matter had been transferred from him to Ali in that regard?" He then answered, in summary, that Abu Bakr was, without dispute, the commander over the people during that pilgrimage, while Ali was the one commanded to make that proclamation. It seems that Ali was unable to make the proclamation alone and needed someone to assist him in it, so Abu Bakr sent Abu Hurairah and others along with him to help him with that.He then cited, through the route of Muharraz bin Abu Hurairah, from his father, who said, "I was with Ali when the Prophet ﷺ sent him with the declaration of disavowal to the people of Makkah, and I used to call it out along with him until my voice grew hoarse, while he used to call it out before me until he grew exhausted." Ahmad narrated it (7977), Ibn Hibban (3820), and others. See Sharh Mushkil Athar (9/225–227).