There's a difference between making up for an existing disparity (the site you linked claims it is doing this and I applaud them for their efforts) and creating a new one (e.g. differential BI).
I don't think there is a single person here who would support giving BI preferentially to men, so when you proposed giving money to women we all assumed you meant giving it preferentially to women, because otherwise your statement would have simply been a restatement of what everyone else was saying. I object to the notion of giving BI preferentially to women, although I fully support the cause of ensuring they receive their share.
This isn't about making up for existing disparity or some form of affirmative action ... it's simply that women seem to be the best investment if you want to impact change on future generations.
Again, you can sit and talk about the "effects" of this or that or you can be involved in helping change someone else's situation[1].
If you're going to do something then you have to look at the evidence available to you. If you've got a village and you give men and women money to help them improve their circumstances and you find out that the majority of men spend the money on themselves (sometimes gambling and alcohol) while the women buy food and spend it on children; what decision would you make?
[1] I set up a free sewing school for WOMEN in India with my father where they take 6 weeks of training and leave with a sewing machine.
The research shows that if mothers obtain the funds they will spend the vast majority on family welfare ~80% whereas the men spend less than 40%.
The difference seems to be attributable to the man having a greater sense of individualism in how they apply the funds and also they incorrectly overestimate their ability spend the funds in profit seeking ways eg gamble the funds or use the funds towards seeking new funds.
I think it's short term vs. long term. Investing in welfare (keeping children clothed, fed and in school) has long term benefits. Unfortunately, that's next to impossible for much of the world.
It's no different from the lottery system here in the US which is used by and marketed to lower income individuals. I don't think anyone says that buying lottery tickets is a "good" investment for a family.