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.
Is blatant misoginy not a good enough reason to downvote?
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 am aware that people, including women, used to use this misoginostic argument. The thing I take issue with is the OP's claim that it's "a good argument", to quote them directly.
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.