  The symmetries and dynamics of simple chiral $SU(N)$ gauge theories, with
matter Weyl fermions in a two-index symmetric tensor and $N+4$ anti-fundamental
representations, are examined, by taking advantage of the recent developments
involving the ideas of generalized symmetries, gauging of discrete center
1-form symmetries and mixed 't Hooft anomalies. This class of models are
particularly interesting because the conventional 't Hooft anomaly matching
constraints allow a chirally symmetric confining vacuum, with no condensates
breaking the $U(1) \times SU(N+4)$ flavor symmetry, and with certain set of
massless baryonlike composite fermions saturating all the associated anomaly
triangles. Our calculations show that in such a vacuum the UV-IR matching of
some $0$-form$-$$1$-form mixed 't Hooft anomalies fails. This implies, for the
theories with even $N$ at least, that a chirally symmetric confining vacuum
contemplated earlier in the literature actually cannot be realized dynamically.
In contrast, a Higgs phase characterized by some gauge-noninvariant bifermion
condensates passes our improved scrutiny.
