  How magnetism emerges in low-dimensional materials such as transition metal
dichalcogenides at the monolayer limit is still an open question. Herein, we
present a comprehensive study of the magnetic properties of single crystal and
monolayer VSe$_{2}$, both experimentally and \emph{ab initio}. Magnetometry,
X-ray magnetic circular dichrosim (XMCD) and \emph{ab initio} calculations
demonstrate that the charge density wave in bulk stoichiometric VSe$_{2.0}$
causes a structural distortion with a strong reduction in the density of sates
at the Fermi level, prompting the system towards a non-magnetic state but on
the verge of a ferromagnetic instability. In the monolayer limit, the
structural rearrangement induces a Peierls distortion with the opening of an
energy gap at the Fermi level and the absence of magnetic order. Control
experiments on defect-induced VSe$_{2-\delta}$ single crystals show a breakdown
of magnetism, discarding vacancies as a possible origin of magnetic order in
VSe$_{2}$.
