We show that strong coupling (SC) of light and matter as it is realized with quantum dots in microcavities differs substantially from the paradigm of atoms in optical cavities. The type of pumping used in semiconductors yields new criteria to achieve SC, with situations where the pump hinders, or on the contrary, favors it. We analyze one of the seminal experimental observation of SC of a quantum dot in a pillar microcavity [Reithmaier, Nature (London) 432, 197 (2004)10.1038/nature02969] as an illustration of our main statements.