Protein-protein interactions (protein functionalities) are mediated by water, which compacts individual proteins and promotes close and temporarily stable large-area protein-protein interfaces. In their classic article, Kyte and Doolittle (KD) concluded that the "simplicity and graphic nature of hydrophobicity scales make them very useful tools for the evaluation of protein structures." In practice, however, attempts to develop hydrophobicity scales (for example, compatible with classical force fields (CFF) in calculating the energetics of protein folding) have encountered many difficulties. Here, we suggest an entirely different approach based on the idea that proteins are self-organized networks, subject to evolving finite-scale criticality (like some network glasses). We test this proposal against two small proteins that are delicately balanced between alpha and alpha/beta structures, with different functions encoded with only 12% of their amino acids. This example explains why protein structure prediction is so challenging, and it provides a severe test for the accuracy and content of hydrophobicity scales. This method confirms KD's evaluation and at the same time suggests that protein structure, dynamics, and function can be best discussed without using CFF.