There's some revisionism going on here. Women did not want to vote. It was the feminism/communism movement that brought on women suffrage. Had the USSR not succeeded in planting this, we likely wouldn't have ever gotten it.
As I understand it, the Women's suffrage movement began mainly in Britain during the late 19th century. The USSR didn't exist until 1922, so I think you've been misinformed.
Arguably, voting rights for some women did exist before then, with Sweden in the 18th century probably being the first. There was also Lydia Taft who was able to vote in colonial America in 1756.