Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as "Quantitative Reasoning" improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.There are two ways of looking at this, but whichever you pick, this analogy doesn't hold up.
First, we can view that what we learn as transferable. This view is consistent with my experience. I went from a BFA in creative writing to a master's in statistics and found that reading and writing about Shakespeare, Twain and Faulkner was good preparation for classes like experimental design and non-parametric methods. I have also found the reverse true: training as a statistician makes you a better critic.**
If problem solving, pattern recognition, logical thinking and other related skills can be transferred to a non-mathematical context then we can make an excellent for teaching more math (though probably not for the way we've been teaching it). If these skills aren't transferable, we can still make a case for math based on statistics and on spreadsheets (everyone has to deal with statistics as a citizen and consumer and every business I've seen could use at least one person who was good on Excel). We can no longer, however, make any kind of case for literature, history or music.
Let's start with literature. It is true that many people read books for enjoyment, but how much effect do literature classes have on what books people read after graduation? The adult recreational reading experience is largely independent of anything learned in school past eighth grade (working under the assumption that a proficient eighth grade reader should be able to handle most of the books people read for pleasure).
We keep teaching literature through high school and include it in the general ed requirements for college because we believe that what students learn in those classes is, to some degree, transferable. If you honestly believe that reading Macbeth does nothing but make you better at reading Elizabethan dialogue, there is no way to justify the waste of class time covering it.
The situation for history is even worse. You can at least make a reading-and-writing case for literature; barring the writing of erudite-sounding op-eds and blog posts, when's the last time you actually needed a historical fact? A few do occasionally come in handy for understanding current events, but the overwhelming majority have no conceivable value unless we assume that students are capable of transferring what they've learned about the long dead to questions regarding the living.
The case for music and art are strictly based on enrichment.
As for politics, I can't rebut this because I'm not sure what he's talking about. Other than a year of junior high civics, we don't really teach politics. We teach courses that are relevant to politics like history, economics and statistics, but the first one requires the students to generalize what they've learned and the last two require lots of you know what.
Professor Ramanathan makes some great points about the marketing of mathematics (read the whole thing) and I'm glad to see national attention brought to the question of what we should be teaching, but it's a complex and subtle question and the professor's Gordian approach isn't going to cut it.
* Along these lines, I did a couple of posts on economics and popular literature here and here and and a post on economics and film criticism here.