Mainly interesting and reasonably plausible, but the bit about female entry into the labour market and wages is almost certainly untrue, something I'd bet practically any economist could agree on. When a woman enters the labour force she adds to demand as well as supply. When this sort of argument comes from someone with other reasons they don't like women working, then it sounds very much like motivated reasoning.Perhaps, though it seems nearly every economist professes to believe that immigration exerts no meaningful downward pressure on wages, too, and I'm unconvinced on that front as well!
In fact, I think there is a lot of overlap in the two fallacies. Adding wage earners will increase total consumer spending, but that's not what anyone outside of GMU cares about. The important issue is whether or not it raises per capita spending power. Annexing Mexico tomorrow would increase the United States' GDP by 8% in one fell swoop, but we'd be a poorer country as a consequence.
If the new wage earners earn more than the existing wage earners, then it is possible (though not necessarily the case) that income per wage earner will increase overall, but if the new wage earners earn less than the existing wage earners--as is overwhelming the case in the US with both women and immigrants--per capita wages are going to stagnate or even decline despite improvements in productivity. Additionally, a growing labor pool and the subsequent increase in competition among wage earners that larger labor pool brings with it, allows those who own the means of production to reap more benefit from productivity gains than those who work for them as employees do. That's been the story for decades now.
Women continue to earn less than men not because of irrational discrimination in the workplace--if that was the case, you or I could get rich tomorrow by starting a firm in an industry where such irrational discrimination is commonplace, overwhelmingly hire the qualified, underpaid women in the field who are getting snubbed, and watch the profits flow in... Okay, that's hyperbolic and oversimplified, and there is of course some level of irrationality in virtually all human affairs, but this sort of irrational discrimination is isolated and marginal in the contemporary scheme of things.
Instead, it is because they are less interested in and less devoted to their careers than men are for obvious biological and cultural reasons--reasons that the vast majority of people instinctively understand. Additionally, they aren't as adept men in industries that pay exceptionally well--primarily those requiring lots of high level math, like engineering and physics.
Parenthetically, immigrants in the US earn less than natives because they tend to be less educated, less intelligent, and less entrepreneurial than indigenous Americans are, and the gap doesn't close even after multiple generations of their descendants have been in the country.