Amyloid proteins are converted from their native-fold to long beta-sheet-rich fibrils in a typical sigmoidal time-dependent protein aggregation curve. This reaction process from monomer or dimer to oligomer to nuclei and then to fibrils is the subject of intense study. The main results of this work are based on the use of a well-studied model amyloid protein, insulin, which has been used in vitro by others. Nine osmolyte molecules, added during the protein aggregation process for the production of amyloid fibrils, slow-down or speed up the process depending on the molecular structure of each osmolyte. Of these, all stabilizing osmolytes (sugars) slow down the aggregation process in the following order: tri > di > monosaccharides, whereas destabilizing osmolytes (urea, guanidium hydrochloride) speed up the aggregation process in a predictable way that fits the trend of all osmolytes. With respect to kinetics, we illustrate, by adapting our earlier reaction model to the insulin system, that the intermediates (trimers, tetramers, pentamers, etc.) are at very low concentrations and that nucleation is orders of magnitude slower than fibril growth. The results are then collated into a cogent explanation using the preferential exclusion and accumulation of osmolytes away from and at the protein surface during nucleation, respectively. Both the heat of solution and the neutral molecular surface area of the osmolytes correlate linearly with two fitting parameters of the kinetic rate model, that is, the lag time and the nucleation rate prior to fibril formation. These kinetic and thermodynamic results support the preferential exclusion model and the existence of oligomers including nuclei and larger structures that could induce toxicity.