That's a perfectly reasonable and straightforward argument which raises eyebrows only because it hints at the idea that feminism had some negative effects.
The comparison to Al-Jazeera might not be sound, however--masculine emotional reserve is a characteristic of Anglo-Saxon/Germanic/Northern European culture, not necessarily Arabic culture.
[1] Feminism, as a natural consequence of advancing the position of women in society, questions gender roles by necessity. This is what makes the reference to Thatcher so inept--Thatcher advanced in a male-dominated profession by following a masculine gender role; Thatcher's Britain was willing to accept a woman PM, but only so long as she governed like a man. This is a far cry from what feminists would like to see.
The basic argument, if I undertand it correctly, is that women should be able to achieve success in any given field by doing things that women are stereotypically interested in. So, for example, they would consider Silicon Valley to be patriarchal because there isn't any role for women who only read People and US Weekly.
I know someone will accuse me of being sexist, but this was actually the consensus from the Women and Entrepreneurship class I took in college, albeit it wasn't phrased in exactly this way.
However, this is unrelated to the grandparent comment, which was (perhaps facetiously) primarily discussing feminism and political correctness, not logical fallacies.
In a male-dominated society, the news is still controlled not by men or women but by money, in the form of advertising revenue.
In a male-dominated society women are stay at home housewives, with time to flip through the channels and shop for household goods, making them a very important consumer demographic and a prime target for advertisers.
Therefore, television news would be 'emotional' and targeted to women.
I don't see how my argument is any less baseless conjecture than yours.
Plus, your counterargument is still pretty flawed--under traditional gender roles, most news is of no interest to women, and wouldn't be targeted to them, which is why news was traditionally aired during evenings, and nights when men were home, while soap operas and talk shows were aired during the day when housewives were home alone. (Come to think of it, your local network affiliate schedule still looks a lot like that.)