He is a liar, and Mālik said, “He was not trustworthy—neither in ḥadīth nor in his religious conduct.” For that reason al-Ḥāfiẓ Ibn Ḥajar, in al-Taqrīb, labelled him “abandoned (matrūk).”
From what has already been shown, the explanation that the mosque was too small is invalid. The view that gains precedence is that of the scholars who stated categorically that performing the prayer in the open prayer-ground (muṣallā) is the Sunnah and remains prescribed in every age and locality except when necessity dictates otherwise. I know of no independent, authoritative scholar who disagreed with this.
Ibn Ḥazm said in al-Muḥallā 5/81: “The Sunnah for the two ʿĪd prayers is that the people of every village or town go out to a spacious open area near their dwellings in the forenoon, after the sun has become bright and at the time when voluntary prayer first becomes permissible.”
He then said (p. 86): “If it is difficult for them to go out to the muṣallā, they should pray together in the congregational mosque.” And he added (p. 87):
“We have transmitted from ʿUmar and ʿUthmān—may Allah be pleased with them both—that they led the people in the ʿĪd prayer inside the mosque because rain fell on the day of ʿĪd. The Messenger of Allah ﷺ, however, used to go out to the muṣallā for the two ʿĪd prayers; that is therefore preferable, while anything else is still valid, for it is an act, not an explicit command. Allah alone grants success.”