Why are not women made pontiffs in Hinduism or in any other religion for that matter?
Three letters written by Sri Vaishnava acharyas opposing ISKCON's decision to appoint female diksha gurus illustrate why Hindu women, in general, cannot become chief priests, acharyas or shankaracharyas. The central issue revolves around whether there is scriptural sanction or established tradition that allows women to initiate others.
Muralidhara Bhattar, Chief Archaka of Sri Ranganatha Swami temple, in his letter, writes:
After reviewing these statements, my conclusion is that the introduction of the female Diksa Guru system in ISKCON will set a bad example to the society of followers of Sanatana Dharma, and it will certainly have wider ramifications for other sampradayas.
Protecting our own sampradayam may include, and is not limited to, withdrawal of the 1970 letter issued by my late father, Sriman Rangaraja Bhattar, on behalf of the Sri Vaishnava sampradayam, certifying that ISKCON is a genuine Vaishnava sampradayam.
As a friend and well-wisher of ISKCON I urge the GBC body to reject this proposal once and for all. Introducing such ashastriya practices will bring about only yoga nashta to the institution.
In another letter to ISKCON, Professor M. A. Lakshmithathachar, the presiding acharya of the Anantarya Peetham, Melkote, writes:
I am deeply concerned with the turmoil that is going on with regards to the mantropadesa and initiation by women preceptors in ISKCON. In a growing organization like ISKCON, confusions, turmoil, statements for and against are bound to prop up. Senior persons at the helm of affairs should go through our ancient texts and try to find out solutions for such problems.
Presently, in the case of permitting women acharyanis, the same procedure has to be adopted. Whatever may be the statements of the shastras, either permitting or prohibiting the acharyanis to do mantropadesa or not, the decision should solely depend upon shistacara. In the history of ISKCON if there is shistacara of mantropadesa by women then acharyanis are free to do mantropadesa. There could be some exceptional cases which might have happened due to the demands of time (āpatkālenāstimaryāda). Exceptions should not become the general rule. Since there is no crisis as to introduce acharyanis to initiate, this should not be considered a serious issue at present.
If ISKCON, an internationally famous organization, goes against the shistacara and be successful, probably the other schools of Vedanta like Ramanuja, Vallabha, Nimbarka, etc., may follow suit, which results in the practice of violating the shishtacara and is not desirable. I wish ISKCON, an internationally reputed organization, will not establish a new shistacara violating all the shistacaras practiced even today in all the schools of Vedanta.
You can read the third letter here.
Interestingly, ISKCON appears to have ignored all these letters and went ahead with their initial decision citing its founder Prabhupāda's commentary on this topic:
Srila Prabhupada severely criticized and warned against bodily and mundane considerations in regard to the role and eligibility of diksa-guru — whether in the form of casteism, selfish motives for profit, adoration or distinction, or as conformity to social, cultural or modern trends and artificial "equality":
...Generally a spiritual master who constantly instructs a disciple in spiritual science becomes his initiating spiritual master later on. (...) Sri Jiva Gosvami advises that one not accept a spiritual master in terms of hereditary or customary social and ecclesiastical conventions. One should simply try to find a genuinely qualified spiritual master for actual advancement in spiritual understanding. (Caitanya-caritamrta, Adi-lila 1.35 purport)