Zevachim 102A

ואין זר רואה את הנגעים! ואם תאמר אהרן הסגירה ⁠– אהרן קרוב הוא, ואין קרוב רואה את הנגעים! אלא כבוד גדול חלק לה הקדוש ברוך הוא למרים אותה שעה: אני כהן ואני מסגירה, אני חולטה ואני פוטרה.

and a non-priest may not inspect the shades of leprous marks to diagnose them. And if you say that Aaron quarantined her, that is difficult, as Aaron was a relative, Miriam’s brother, and a relative may not inspect the shades of leprous marks. Rather, God bestowed a great honor on Miriam at that time, and said: I Myself am a priest, and I will quarantine her for 7 days to see if the shades of leprous marks persist, and I will declare her a metzora if she is impure, and I will exempt her if she is not impure.

קתני מיהת: משה זר, ואין זר רואה את הנגעים!

In any event, the midrash teaches: Moses was a non-priest, and a non-priest may not inspect the shades of leprous marks, which contradicts the statement of Rav that Moses was a priest.

אמר רב נחמן בר יצחק: שאני מראות נגעים, דאהרן ובניו כתובין בפרשה.

Rav Naḥman bar Yitzḥak said: The halakhot of the examination of shades of leprous marks are different, because specifically Aaron and his sons, and not Moses, are written in the passage that discusses them: “Then he should be brought to Aaron the priest, or to one of his sons the priests” (Leviticus 13:2). Therefore, there is no proof from this baraita that Moses was not a priest.

מיתיבי: חמש שמחות היתה אלישבע יתירה על בנות ישראל ⁠– יבמה מלך, אישה כהן גדול, בנה סגן, בן בנה משוח מלחמה, ואחיה נשיא שבט; ואבילה על שני בניה.

The Talmud raises an objection to Rav’s statement from a baraita: Elisheva, the daughter of Amminadav and the wife of Aaron, had 5 more reasons for joy than the other daughters of Israel on the day the Tabernacle was dedicated: Her brother-in-law, Moses, was a king; her husband, Aaron, was the High Priest; her son, Elazar, was the deputy High Priest; her son’s son, Pinehas, was the priest anointed for war, who would lead the army out to battle; and her brother, Nahshon, son of Amminadav, was the prince of the tribe of Judah, who brought his offering on that day, as the first of all the princes. But on that same day of joy she was in mourning for her two sons, Nadav and Avihu, who died on that day.