"For his mother" is extra for a Gezeirah Shavah (we cannot learn from a Gezeirah Shavah unless the words in (at least) one of the sides are free (unnecessary);

(Beraisa - Rebbi) Question: A Nazir may not be Metamei for his relatives "in their death", but he may be Metamei through their leprosy or emissions. What is the source for this regarding a Kohen Gadol?

Answer: It was not needed to write "for his mother" regarding a Kohen Gadol.

A regular Kohen may be Metamei for his paternal brother, but a Kohen Gadol may not be Metamei for his father. A regular Kohen may not be Metamei for his maternal brother, so all the more so, a Kohen Gadol may not be Metamei for his mother!

Since we can learn from a Kal v'Chomer, "for his mother" is free for a Gezeirah Shavah.

It also says "for his mother" regarding a Nazir. Just like a Nazir may be Metamei through relatives' leprosy or emissions, but not their corpses, also a Kohen Gadol.

Question: We expounded that a Kohen Gadol may be Metamei for a Mes Mitzvah. What is the source regarding a Nazir?

Answer (Beraisa) Suggestion: Perhaps "...Al Nefesh Mes Lo Yavo" refers even to an animal, which is called "Nefesh Beheimah"!

Rejection #1: "Al Nefesh Mes" refers to a person.

Rejection #2 (R. Yishmael): We need not learn from there. "Lo Yavo" discusses a Tum'ah imparted by entering (an Ohel).

(Continuation of Beraisa): "For his father and for his mother" he may not be Metamei, but he may be Metamei for a Mes Mitzvah.

Question: Why must the verse teach this? A Kal v'Chomer teaches this!

A Kohen Gadol's Kedushah is permanent, and he may be Metamei for a Mes Mitzvah. All the more so, a Nazir may, for his Kedushah is temporary!

Answer: The Kal v'Chomer can be challenged. A Kohen Gadol may be Metamei because he does not bring a Korban for Tum'ah, but a Nazir brings a Korban for Tum'ah!

Therefore, we need a verse to permit him to be Metamei for a Mes Mitzvah.

Suggestion: Perhaps we should expound that he may not be Metamei for a parent, but he may for others (strangers)!

Rejection: A regular Kohen may be Metamei for relatives, but not for strangers. A Nazir may not be Metamei for relatives, all the more so he may not for strangers.

Therefore, the verse forbids Tum'ah for a parent, and permits for a Mes Mitzvah.

Question: We should be able to learn from a Kohen Gadol!

The Torah teaches that a Kohen Gadol may not be Metamei for relatives, and also regarding a Nazir. Just like a Kohen Gadol may be Metamei for a Mes Mitzvah, we should say the same for a Nazir!

Answer: We might have thought that we should learn from a regular Kohen!

The Torah teaches that a regular Kohen may not be Metamei, and also regarding a Nazir;

Just like a regular Kohen may be Metamei for relatives, we should say the same about a Nazir!

Conclusion: Since we would not know if we should learn a Nazir from a Kohen Gadol or from a regular Kohen, the verse is needed to forbid Tum'ah for a parent, and to permit for a Mes Mitzvah.

Question: Since we need to learn that he may not be Metamei for a parent, we cannot also learn that he may be Metamei for a Mes Mitzvah!

Answer: Rather, "for his father" forbids Tum'ah for his father. "For his brother" he may not be Metamei, but he may be Metamei for a Mes Mitzvah.

"For his mother" is used for the Gezeirah Shavah, like Rebbi taught.

Question: What does "for his sister" teach?

Answer (Beraisa) Suggestion: If a man (not necessarily a Nazir) was going to slaughter his Korban Pesach or circumcise his son, and he heard that a relative died, perhaps he should be Metamei to bury the relative!

Rejection: "For his sister" he may not be Metamei, but he may be Metamei for a Mes Mitzvah.

R. Akiva says "A soul (this is the correct text, for he expounds the verse by Nazir)" forbids Tum'ah for strangers. "Mes" forbids Tum'ah for relatives;

"For his father and for his mother" he may not be Metamei, but he may be Metamei for a Mes Mitzvah;

"For his brother" teaches that a Nazir Kohen Gadol may not be Metamei for his brother, but he may be Metamei for a Mes Mitzvah.

"For his sister" teaches like the Beraisa, i.e. if a man was going to slaughter his Korban Pesach or circumcise his son...

Question: How does R. Akiva learn Rebbi's Gezeirah Shavah?

Answer: Since "for his brother" permits a Nazir Kohen Gadol to be Metamei for a Mes Mitzvah, surely the same applies to any Kohen Gadol;

"For his father and to his mother" is free for the Gezeirah Shavah.

Question: How does R. Yishmael learn that a Nazir Kohen Gadol may be Metamei for a Mes Mitzvah?

Answer: Since the Torah permitted a Lav (for a Kohen Gadol or Nazir) for a Mes Mitzvah, also two Lavim are permitted.

Question: What does R. Yishmael learn from "for his sister"?

Answer: One might have thought that a Mes Mitzvah overrides only Lavim, but not Korban Pesach or circumcision, which are punishable by Kares for one who neglects to do them;

The verse teaches that a Mes Mitzvah overrides even these.