Whats does this means in "The institutes of vishnu book" :
- A woman who keeps a fast or performs a penance in the lifetime of her lord, deprives her husband of his life, and will go to hell.
Is women fasting a sin?
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Whenever any smiriti talks about no sacrifice for women, they means that they can't sacrifice alone. Even husband can't perform sacrifice without her wife.
Atharvaved 12:3:1"O men! sit on your place for sacrifice and take your wife with you. The couple who performed this ritual before and your reward will be same."[Shri Ram Sharma]
So Vedas say that men has to perform ritual with his wife.
Taittiriya Brahmana (22.214.171.124) “A man who has no wife is not entitled to sacrifice”
Skanda Purana IV.i.4.68 “Two worlds, viz. the visible world and the other world are won over through wife. A man without a wife is not entitled to perform the rites of Yajna pertaining to gods, manes and guests.”
The book you are quoting is a smriti(Vishnu Smriti). Even if you think that women should not perform sacrifice in Smriti, so the Smriti is wrong because they are opposing Vedas. And smritis themselve says that anything apart from Vedas shouldn't be followed.
Manusmriti 12:"95. All those traditions (smriti) and those despicable systems of philosophy, which are not based on the Veda, produce no re- ward after death; for they are declared to be founded on Darkness. 96. All those (doctrines), diering from the (Veda), which spring up and (soon) perish, are worthless and false, because they are of modern date."
So even smritis are sacred but if they contradict Vedas, they should be rejected.
You have to read it in connection with immediately preceding statement:
- No sacrifice, no penance, and no fasting is allowed to women apart from their husbands...
And then comes your statement:
- A woman who keeps a fast or performs a penance in the lifetime of her lord...
It means that fasting without permission of husband, or holding a different vrat that her husband/in-laws do not, is not recommended for wives.
Of course, the exception to this rule might be Devi Savitri, who insisted on keeping vrat without informing husband why, because she knew about his jataka curse but he did not, and thus was able to save him from Yama.