It is my understanding that the decision to give a get was the husband’s. A wife might ask for one but she usually needed her husband’s consent.

As more European Jews came to the US, husbands often used the threat of refusing to give a get in order to get a very favorable civil divorce settlement. Over time, in places like NY, judges had to deal with that Jewish issue. I believe they ordered men to give their wives a get. Without a get, a religious woman could not remarry in the eyes of the community.
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Shelley Mitchell 
NYC
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