  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.
