I run a small farm, and I've been a professional programmer for about 12 years. I agree with what you say - kids should definitely have the opportunity to learn both. Of my two pursuits above, farming is much newer to me and I've found an amazing amount of skill transfer from the world of programming to the world of farming. Granted, my sheep don't understand when I yell at them in haskell, but the approaches to problem solving, whole-system thinking, and consideration of edge cases I think are enormously beneficial in almost any profession.
I do think that today's kids would benefit not only from knowing a thing or two about how to raise some food (very different from actual "farming") and also from having much more contact with the natural world.
I also think that many kids would benefit from learning the "art" side of programming - the stuff that's fun and interesting, like solving puzzles, appreciation of the hard-to-define idea of elegance, reverse engineering, etc. Nothing else I've learned to do has had quite the impact on my ability to consider many angles in a situation and reason a way to get from one state to another, and at least for me it's been a fun process to learn it all.
My real complaint when anybody says "Everybody should have to learn X," is that I think it should be "Everybody should have a chance to learn X." Coding was the best path for me to learn to think about complex, abstract things and apply that thinking to the real world (including farming). For others, it may not be so.