I don't know why you're being downvoted, this has been one of the arguments of anti-suffragist groups which, by the way, heavily comprised of women until it became completely unfashionable.
The poster above is claiming that women are more easily influenced by social pressure to vote against their interests. This is blatant and unacceptable misoginy.
I also very much doubt your claim that most anti-suffragists were women. Especially since women had no power to decide something like this at the time - since only men voted, and only men could hold positions of authority, it was only men who could prevent women from being allowed to vote.