FLASH radiotherapy has the potential to improve both patient quality of life and outcomes by delivering radiation at ultrahigh dose rates to effectively target tumours while sparing healthy tissues. However, the differential sensitivity of healthy tissues versus tumours to FLASH radiotherapy remains unexplained. In this Perspective, we hypothesize that FLASH radiotherapy distinguishes healthy tissues from tumours based on subtle functional and structural biological differences. We identify commonalities present in the various healthy tissues that are spared by FLASH radiotherapy that might be lost during tumorigenesis. We also propose that a specific class of proteins, termed long-lived proteins, define a critical radiolytic target that are present in nearly every healthy tissue that is FLASH radiotherapy resistant yet are absent in tumours. We extend this structural hypothesis further by suggesting that tumour and extracellular matrix rigidity affects sensitivity to changes in radiotherapy dose rate, where more rigid and dense desmoplastic tumours are more sensitive to FLASH radiotherapy than those possessing more elasticity. Substantiating these concepts experimentally may provide a new and generalized mechanism of action of radiation effects and may therefore inform clinical trial designs by identifying those tumour subclasses expected to exhibit optimal responses to FLASH radiotherapy.