There are several reasons women in Switzerland gained the right to vote only in 1971. The main reason is the direct democracy. There had to be a referendum to give women the right to vote. It’s quite likely that many countries would have introduced the women suffrage later.
Another reason is there was political continuity in Switzerland and no direct involvement in the world-wars. In many countries women suffrage got introduced after the wars and as part of a new constitution. The Swiss Women’s Movement wasn’t as radical as in other countries. They tried to educate and debate their countrymen, which did not work. They also weren’t as tightly linked to the socialists as in other countries. In places were they did, like in the west, the movement was more successful.
Here you can find a nice collection of posters.
The last canton to introduce women suffrage, Appenzell Innerrhoden, had a vote in 1989 and rejected granting voting rights. Some people sued and the Federal court ruled against the canton. In 1991 women voted the first time at the Appenzeller Landsgemeinde.