  EuCd$_2$As$_2$ is now widely accepted as a topological semimetal in which a
Weyl phase is induced by an external magnetic field. We challenge this view
through firm experimental evidence using a combination of electronic transport,
optical spectroscopy and excited-state photoemission spectroscopy. We show that
the EuCd$_2$As$_2$ is in fact a semiconductor with a gap of 0.77 eV. We show
that the externally applied magnetic field has a profound impact on the
electronic band structure of this system. This is manifested by a huge decrease
of the observed band gap, as large as 125~meV at 2~T, and consequently, by a
giant redshift of the interband absorption edge. However, the semiconductor
nature of the material remains preserved. EuCd$_2$As$_2$ is therefore a
magnetic semiconductor rather than a Dirac or Weyl semimetal, as suggested by
{\em ab initio} computations carried out within the local spin-density
approximation.
