I’m not the original parent, but I read (and share) the position as:
Barring intent by the speaker to inflict direct and immediate physical harm, if you are too frail to maintain your mental health in the face of someone else’s speech (or you pretend to be), then you are not served — and neither is justice, fairness, or truth — by the state applying its monopoly on violence to forcibly silence others at your behest.
Instead, each individual is personally responsible for their own mental well-being, while the state’s responsibility extends no further than offering services and support to help enable your own individual resiliency.