American voters granted women the right to vote in 1920. By that time, women in New Zealand had been voting for 27 years.
New Zealand was different from the United States in several key ways:
Women were already used to helping men much more, in business and on the farm. New Zealand was a rugged land, settled by Europeans later in history than the U.S. It wasn't an equal man-woman partnership, but New Zealand women did have the benefit of living in a society that was slightly more enlightened.
Because of this, more women in New Zealand were educated, at an earlier age. This led to asking more questions, about their role in society and in government.
Many women were involved in an anti-alcohol movement in the late 19th Century. Just as in America and Britain, New Zealand had a Women's Christian Temperance Union. One of the main aims of this organization was to get laws passed that would control the alcohol abuse that was common in much of society. Many of these women discovered that they could work their hardest to get a law passed or changed but couldn't then do anything more about it; they still had to leave it up to men to to the final part of the job. It wasn't long before women started wanting to vote on laws themselves and to be a part of the government.
New Zealand was a smaller country than the U.S., both in land mass and population. It was a rural country, yes, but it was, for the most part, easier to organize a concerted effort to win the right to vote in a smaller, less populous country.
New Zealand was also a relatively new country. British colonists had come to America to stay way back in 1607, beginning with the Jamestown colony. Settlers in New Zealand didn't arrive to stay really until the 1800s. By this time, the idea of having women play more of an equal role in certain parts of their lives didn't seem all that strange, especially since the women's vote movement was going strong in Great Britain at this time, too. Thus, the climate for change along these lines was better in New Zealand than in America, where men were entrenched in their beliefs and their traditions.