Teaching chemistry to non-majors is challenging mainly because students don't feel the need to know. Why should a student that is thinking about pursuing careers in biology, pharmacy, medicine, physical therapy, or any other field in the health sciences needs to know about the periodic table, bond energies, or Gibbs free energy? The simpler answer is of course: because....
When framed within today's perception that knowledge should be utilitarian in the sense of direct practicability is difficult to answer the question, but looking from a wider perspective and knowing that learning topics based on immediate use is shortsighted we could try to answer the question by saying: It is not about the topic but about the process that leads to the knowledge of that topic. What I mean by this is that even though learning about the quantum model of electronic behavior around the atom may not have immediate use, comprehending how the model is developed and used in the understanding of the chemical behavior of elements in nature is the basis of a deeper level of thinking what one could call "complex-higher level" analysis.
The advantages of this higher level of thinking will undoubtedly be advantageous for students later in their career, when they will have to face challenges requiring this sort of analysis. It will be outside the realm of chemistry but the fundamental structure of the situation requiring solution will be similar to the structure of the problem analyzed in chemistry.
Further arguments are based on the perception that one can be a good user of ideas even if one lacks deep understanding of their history and evolution, but one will never be able to improve the use of these ideas or to innovate these ideas or to create different ideas in this field without that deepness on understanding. A pharmacist will be able to administer medicines prescribed by a doctor just by following the instructions on a prescription without understanding the bio-chemical functionality of the chemicals. But the pharmacist will not be able to know and therefore recommend a proper use of these medications when other medicines have been administered to the patient. This is extremely important as we now know that any medicine will have some secondary effects on the patient and it could be dangerous -in fact, in some cases with extreme consequences. It seems that is taken for granted that if the pharmacist is working in industry related to the development of medications, hir knowledge of bio-chemistry is fundamental.
The same could be mentioned about biology. One could argue that in order for a biologist to perform in hir field, say by studying plants, the only thing s/he needs is either a good memory (to remember all classification of species) or most likely today good access to the information but not how the cells in the organism is being fed. Of course that is false! As we know today in order to understand how an organism functions we must understand each individual organ works. In turn that means going all the way deeper into understanding how each organ is made of cells and these made of bio-chemicals, and these made of atoms.
This is where I get my chance to play, it is my turn when someone is asking questions about the how and why of a process in the natural world. So my roll as a chemistry professor is to facilitate a connection between everyday in my students life with every concept developed in class. This is why at the end of each semester I ask my students to write a short paper where they describe one or two concepts learned in class that relate to something they consider important or relevant in their lives.