Bukhari

Hadith Commentary:
Imam Ahmad, acting upon the apparent meaning of the hadith, stated that this ruling is obligatory (wujuban). This is because jihad can be performed by other Muslims as a substitute, but with his wife, no one except a mahram can go.

Hadith Commentary:
(1)
It is obligatory upon the husband to protect and safeguard his wife; therefore, it is necessary for him to accompany her for Hajj. The obligation of jihad can be fulfilled by others and substitutes can be found for it, but no one except a mahram can accompany a woman.
(2)
It is also understood from this hadith that if a woman does not have a mahram with her, Hajj is not obligatory upon her, no matter how wealthy she may be.
(‘Umdat al-Qari: 14/208)

Hadith Commentary:
Because another man cannot go to his wife in his place, whereas in jihad another person can participate as his substitute, so the Prophet (sallallahu alayhi wa sallam) gave precedence to the necessary duty over the non-essential one.
A woman possesses an independent status in her own person.
Therefore, she may perform Hajj herself with her own wealth.
However, it is necessary for her husband to accompany her, or for her to be accompanied by a mahram (close male relative) sent on his behalf.

Hadith Commentary:
➊
A mahram is a person with whom marriage is permanently forbidden. A woman is not permitted to travel without a mahram.
➋
From this hadith, it is understood that if a person’s name is written for jihad and his wife intends to perform Hajj, then he should accompany his wife. It is not obligatory for him to go for jihad, because in jihad someone else can take his place, but for accompanying his wife, no stranger can be a substitute.
➌
This hadith also shows that important matters should be given precedence over temporary affairs, because the Messenger of Allah (sallallahu alayhi wa sallam) gave importance to a necessary matter. Thus, in the case of a conflict between the journey of Hajj and the journey of jihad, he gave preference to the journey of Hajj.

Hadith Commentary:
Benefits and Issues:
From this hadith, it is understood that if a husband is able to accompany his wife for Hajj, then he should abandon such an obligation for which there is no fixed time, or for which another person can take his place.

587 Lexical Explanation:

«لَايَخُلُونَّ» This is the prohibitive form from «خلوة» with the emphatic "noon" (nun al-tawkid).
«ذُو مَحْرَمٟ» The "meem" and "raa" have a fatha (zabar) on them, and between them the "haa" is sakin (quiescent). By this are meant those close relatives of a woman with whom marriage is forbidden to her, such as father, son, brother, etc.
«اُكْتُتِبْتُ» This is the first person passive form from the verb pattern "ifti‘aal," meaning "my name is included in the list of the mujahideen and I have been designated for such-and-such expedition." This hadith is evidence that a woman cannot perform Hajj without her husband or a mahram (unmarriageable kin), and for a woman this is also, in general, included in the ruling of «مَنِ اسْتَطَاعَ اِلَيْهِ سَبِيْلًا». This is an additional condition for a woman: if it is fulfilled, Hajj becomes obligatory upon her; otherwise, the obligation of Hajj does not apply to her.

Benefits and Issues:
➊ This hadith establishes that it is forbidden (haram) for a non-mahram man and woman to be alone together in seclusion (khalwah). In fact, in another hadith it is stated: "Whenever the two are alone, the third among them is Shaytan." Similarly, it is also forbidden for a woman to travel alone without a mahram. Some jurists, based on certain evidences, have permitted this for an elderly woman, in the case of a caravan, or for a woman of high status, but the explicit wording of the hadith negates this.
➋ This hadith also shows that if Hajj is obligatory upon a woman, then, like prayer, she does not need her husband's permission. However, if it is a voluntary (nafl) Hajj, then in any case, the woman should obtain permission before going.