  We critically examine the recent claim that the Standard Model Higgs boson
${\cal H}$ could drive inflation in agreement with observations if $|{\cal
H}|^2$ has a strong coupling $\xi\sim 10^4$ to the Ricci curvature scalar. We
first show that the effective theory approach upon which that claim is based
ceases to be valid beyond a cutoff scale $\Lambda=m_p/\xi$, where $m_p$ is the
reduced Planck mass. We then argue that knowing the Higgs potential profile for
the field values relevant for inflation ($|{\cal H}|>m_p/\sqrt{\xi}\gg
\Lambda$) requires knowledge of the ultraviolet completion of the SM beyond
$\Lambda$. In absence of such microscopic theory, the extrapolation of the pure
SM potential beyond $\Lambda$ is unwarranted and the scenario is akin to other
ad-hoc inflaton potentials afflicted with significant fine-tuning. The
appealing naturalness of this minimal proposal is therefore lost.
