Having spent countless hours in grad school arguing about frequentist and Bayesian statistics, I appreciate Richard D. Morey’s take on the importance of p values:
The mistake many statistical commentators make is to interpret the p value as attempt at a quantification of evidence, or as a posterior probability. It is none of these things, nor is it meant to be. It should not even, really, be thought of as means to make an inference (although, it is in the most simplistic interpretation of the Neyman-Pearson paradigm). It is, instead, a means to critique a potential inference.