regarding the Prophet's birthday (unclear)?

The Shaykh : We mentioned that honoring a legal ruling requires proof, and this is the case with the exaltation of the Prophet's (peace and blessings be upon him) birthday as people do today. Furthermore, the Prophet (peace and blessings be upon him) did not mention the day of the month on which he was born; he mentioned the day of the week. Do these people consider it by the day of the week or by the month? By the month. We also mentioned that it is not established that the Prophet (peace and blessings be upon him) was born on the twelfth day, and that some contemporary researchers have verified that his birth was on the ninth day.