I always point out that subjects like algebra and geometry teach how to think (for example, in a logical stepwise fashion) and how to see non-obvious relationships between things.
Your argument for studying algebra and geometry hinges on the existence of "transfer", which is plausible but which has been controversial in research on education. The book "Transfer on Trial" by Detterman
http://www.amazon.com/Transfer-Trial-Intelligence-Cognition-Instruction/dp/0893918261 looks at the research.
But part of me wonders about the kinds of adults who make comments about the pointlessness of certain subjects. I can understand this attitude in kids, but not adults. So I think that my ideas are usually best aimed at kids, who probably don't have the perspective to understand why these things are important.
Adults might just get offended.
A pleasure of having young children is that one need not weigh the practicality of their interests but can just encourage them in whatever direction interests them. My 5yo is fascinated by dinosaurs, so we borrow and buy books on dinosaurs. But given the tough job market (especially for new entrants) and the exorbitant cost of private colleges, especially for affluent families, it's not surprising that parents forking over $200K+ want to know how college courses taken will lead to a good job. I'd have real reservations about having my children major in, for example, folklore and mythology http://web.me.com/folkmyth/Folk_%26_Myth/Welcome.html .
