Polar cosolvents are commonly used to guide the self-assembly of amphiphiles in water. Here we investigate the influence of the cosolvent acetonitrile (ACN) on the structure and dynamics of a supramolecular polymer in water, which is based on the well-known benzene-1,3,5-tricarboxamide motif. Hydrogen/deuterium exchange mass spectroscopy measurements show that a gradual increase in the amount of ACN results in a gradual increase in the exchange dynamics of the monomers. In contrast, the morphology of the supramolecular polymers remains unchanged up to 15% of ACN, but then an abrupt change occurs and spherical aggregates are formed. Remarkably, this abrupt change coincides with the formation of micro-heterogeneity in the water-ACN mixtures. The results illustrate that in order to completely characterize supramolecular polymers it is important to add time-resolved measurements that probe their dynamic behavior, to the conventional techniques that are used to assess the morphology of the polymers. Subsequently we have used time-resolved measurements to investigate the influence of the concentration of ACN on the polymerization and depolymerization rates of the supramolecular polymers. Polymerization occurs within minutes when molecularly dissolved monomers are injected from ACN into water and is independent of the fraction of ACN up to 15%. In the depolymerization experiments - initiated by mixing equilibrated supramolecular polymers with dissolved monomers - the equilibration of the system takes multiple hours and does depend on the fraction of ACN. Interestingly, the longest equilibration time of the polymers is observed at a critical solvent composition of around 15% ACN. The differences in the timescales detected in the polymerization and depolymerization experiments are likely correlated to the non-covalent interactions involved, namely the hydrophobic effect and hydrogen-bonding interactions. We attribute the observed fast kinetics in the polymerization reactions to the hydrophobic effect, whereas the formation of intermolecular hydrogen bonds is the retarding factor in the equilibration of the polymers in the depolymerization experiments. Molecular dynamics simulations show that the latter is a likely explanation because ACN interferes with the hydrogen bonds and loosens the internal structure of the polymers. Our results highlight the importance of the solution conditions during the non-covalent synthesis of supramolecular polymers, as well as after equilibration of the polymers.