The claim was that big government was the root of most of our current problems and women in turn tend to vote for bigger government (and socialism but I used the lower case s on socialism which does not mean the Socialist party, it means a diverse group of potential policies that are all characterized by some group that isn't an individual and is usually the government owning some subset of assets and providing some subset of services)
Go look at the polling records across time and you see women voting for bigger government by way of voting for groups that have policies that ensure larger government (they are not the only group doing this, they are just the group we are talking about now. Single men also lean problematic in their voting patterns for example).
Talking about the Socialist party here is the wrong metric to use because it encompassed truly nutty groups that had no chance of being elected (from agricultural commune supporters to straight up communists). If you look at the subsets that actually got elected (i.e. the sewer socialists) they ran on policies like old age pensions, employment insurance, public housing, public health care and other big government welfare programs. Pretty much all this stuff had been subsumed into the big parties by the 1960's and was actually being implemented, so why would you ever expect the Socialist party to continue existing? All their electable policies (that became much more electable with women gaining the right to vote) were adopted by mainstream, usually democrat candidates who subsequently were elected. Subsequently all these programs form part of the big government problem we have today.
You see the above in the USA but you also see it in my home country of Canada, most recently with the current oaf running things federally, who has been kept in power by women voters not changing their vote when it became obvious he was doing likely criminal things while pursuing a suicidal spending platform at home and making us the laughing stock of the world stage with his antics.
Anyways, this is not to say women shouldn't have the vote, they very clearly should have the vote. My original post was mostly about how we integrate the clearly correct idea that women should be able to vote with the clearly correct idea that their voting patterns are causing a lot of our current problems. I think the actual correct solution is some other system of limiting suffrage to only those who clearly have long term skin in the game, as to what that would look like I am not certain. It could take the form of limiting voting to citizens who currently have at least 50 % custody/responsibility for a child of theirs or have X number of years of at least 50% custody/responsibility for a child of their under their belts. Or perhaps requiring citizens to post an income adjust long term bond to vote and have that bond be the first risk of loss if the government runs a deficit of a certain amount for more than 1 year. The challenge with limiting suffrage is having the rule be simple enough that gaming it is very difficult, while being strong enough to actually cut out enough of the people with no incentive to think long term about the country that they can't drive us into bureaucratic ruin.