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 behaviour 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 non-decoupling 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 show that not only a 2HDM where the lightest of the CP-even scalars is the 125 GeV one does not require new physics to be stable up to the Planck scale but this is also true when the heavy CP-even Higgs is the 125 GeV and the theory has no decoupling limit for the type I model.
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