The two-Higgs-doublet model (2HDM) provides an excellent benchmark to study physics beyond the Standard Model (SM). In this work, we discuss how the behavior of the model at high-energy scales causes it to have a scalar with properties very similar to those of the SM—which means the 2HDM can be seen to naturally favor a decoupling or alignment limit. For a type II 2HDM, we show that requiring the model to be theoretically valid up to a scale of 1 TeV, by studying the renormalization group equations (RGE) of the parameters of the model, causes a significant reduction in the allowed magnitude of the quartic couplings. This, combined with B-physics bounds, forces the model to be naturally decoupled. As a consequence, any nondecoupling limits in type II, like the wrong-sign scenario, are excluded. On the contrary, even with the very constraining limits for the Higgs couplings from the LHC, the type I model can deviate substantially from alignment. An RGE analysis similar to that made for type II shows, however, that requiring a single scalar to be heavier than about 500 GeV would be sufficient for the model to be decoupled. Finally, we ... mehrshow that the 2HDM is stable up to the Planck scale independently of which of the CP-even scalars is the discovered 125 GeV Higgs boson.