  We study non-abelian gauge theories with fermions in a representation such
that the surviving electric 1-form symmetry is $\mathbb{Z}_2$. This includes
$SU(N)$ gauge theories with matter in the (anti)symmetric and $N$ even, and
$USp(2N)$ with a Weyl fermion in the adjoint, i.e. ${\cal N}=1$ SYM. We study
the mixed 't Hooft anomaly between the discrete axial symmetry and the 1-form
symmetry and show that when it is non-trivial, it leads to non-invertible
symmetries upon gauging the $\mathbb{Z}_2$. The TQFT dressing the
non-invertible symmetry defects is universal to all the cases we study, namely
it is always a $U(1)_2$ CS theory coupled to the $\mathbb{Z}_2$ 2-form gauge
field. We uncover a pattern where the presence or not of non-invertible defects
depends on the rank of the gauge group.
