So how did female voting increase government spending before 1980 without a majority?
Leaving aside the huge issues regarding the question background, let me address the question as asked.
It is absolutely not necessary that a subgroup of the electorate be a majority before they influence policy. Thinking this would seem to imply a picture in which ALL men are in favour of smaller government spending and ALL women are in favour of more government spending. This is clearly not the case, and can be demonstrated by a cursory glance at opinion polls on the subject.
To take a massively oversimplified answer imagine that there is a gender divide in how men and women think about government spending. I'm not saying that is actually the case, just citing an example. Let's imagine 45% of men are in favour of higher spending, and 75% of women. If 20% of women vote that is enough to push the "higher spending" vote to 50%.
In reality of course the question of "higher spending" is much more complicated. Nobody votes for "higher government spending". They vote for certain programs, and higher government spending is a result of that. There are other programs those same people would not support, and so money does not get spent on those, resulting in lower government spending.
Also the two charts contradict each other. The first says (about 1920) "instantly spending is higher than revenue". The commentary says (again about after 1920) "US debt rose and rose". But the second chart shows that debt declined between 1946 and 1982, meaning expenditure was not higher than revenue. At least one of things shown is wrong.
TLDR; The meme is self-contradictory. The question is a simple misunderstanding of math and the electoral system.
P.S. It's worth pointing out that while the infographic is very questionable, the referenced article is scholarly and reasonable, and goes into some depth on the societal reasons why more women vote for higher government program funding than men.