My message must have been unclear, because you think you disagree with me, but I completely agree with you :)
Let me just say: math is wonderful. Science is wonderful. You're absolutely right that math provides a rich source of models and metaphors for understanding the most diverse domains. Everyone should study them!
Yet I don't feel the need to sing the praises of math and science. Why? Because nobody doubts their value. But people do question the value of the humanities. They even imply that they are worthless and should be eliminated. And that seriously concerns me, because in my opinion, they are invaluable. They represent a huge portion of our cultural inheritance, and yes, they teach things that are not found in STEM subjects.
Two important things that the humanities teach are history (knowing how we got here and why) and what I previously called "critical thinking". I realize now that that term is too ambiguous. People think I mean something like "good thinking" or "novel thinking", which are certainly present in STEM as well.
What I intended is much more specific than that. It's the ability to question our assumptions about ends. Science asks about how things are. The humanities ask about how things ought to be. It's an alltogether different domain of inquiry.
Whether it is literature, philosophy, painting, or theater, a humanistic work proposes an ideal for human life. Over time, great works in the humanities dramatically alter our collective understanding of what is good and worthwhile. They help us ponder our destiny.
Popular culture does not do that for us. It is driven by business interests and rarely makes detours into the pursuit of serious questions. The humanities do. They are our sincerest and most persistent attempt to get to the bottom of what really matters.