Symmetries can clash with quantum mechanics (anomalies) — and there are several kinds. A gauge anomaly makes a theory inconsistent, so it must cancel: in the Standard Model the gauge and mixed gauge–gravitational anomalies cancel generation by generation, which fixes the hypercharges. A 't Hooft anomaly of a global symmetry is not an inconsistency but an obstruction to gauging it; it cannot change along the RG flow, so it constrains strongly coupled dynamics. The ABJ anomaly is what a mixed 't Hooft anomaly becomes once the other symmetry is gauged: the axial U(1) of QED has a mixed anomaly with the vector U(1); gauging the vector one (electromagnetism) breaks the axial one explicitly, $\partial_\mu j^\mu_A \propto F\tilde F$ — the origin of $\pi^0\to\gamma\gamma$. Full taxonomy (gravitational, global, trace anomalies) in Symmetries & Generalized Symmetries.