Cancer immunotherapy by checkpoint blockade (ICB) is effective for various cancer types, yet its clinical use is encumbered by a high variability of patient response. Several studies have reported that the number of non-synonymous mutations (Tumor Mutational Burden, TMB), can predict patient response to ICB. This belief has become widespread and led to the FDA approval of immunotherapy patient prioritization based on TMB levels. The notion that TMB is predictive of response to immunotherapy is rooted in the neoantigen theory which stipulates that cancer-specific mutations can form neoantigens, which can be recognized by the immune system. Hence, the more mutations a tumor has, the more likely the immune response can be triggered. Here we revisit the data underlying the reported TMB/ICB response association and the neoantigen theory. First we assembled the largest pan-cancer dataset of immunotherapy patients with sequencing and clinical data. Surprisingly, we find little evidence that TMB is predictive of response to ICB. We demonstrate that associations similar to the ones reported previously can be observed in shuffled data, suggesting that previous studies suffered from the lack of correction for multiple hypotheses testing and confounding disease subtypes. Second, we revisit the neoantigen theory and demonstrate that a simple mathematical model can be consistent with both immunogenicity of neoantigens and the lack of association between TMB and response. Our analysis shows that the use of TMB in clinical practice is not supported by available data and can deprive patients of treatment to which they are likely to respond.