One of the big voices against giving women the vote was the organization National Association OPPOSED to Woman Suffrage. In the 1910s it published this pamphlet explaining why women shouldn’t be allowed to vote:
BECAUSE 90% of the women either do not want it, or do not care.
BECAUSE it means competition of women with men instead of co-operation.
BECAUSE 80% of the women eligible to vote are married and can only double or annul their husband’s votes.
BECAUSE it can be of no benefit commensurate with the additional expense involved.
BECAUSE in some States more voting women than voting men will place the Government under petticoat rule.
BECAUSE it is unwise to risk the good we already have for the evil which may occur.
Cultural change is much slower than I think most would prefer (well, unless you’re the Taliban or of similar inclinations) but it’s worth seeing things like this to remember that not even that long ago, as absurd as it seems today, this kind of opinion was actually a mainstream opinion.