I'd imagine the person walking his dog was making the area no less safe for anyone else. Maybe people might feel safer.
The rule, in the abstract, can be given some plausible 'social good' defense -- many rules can, even the most insidious. No doubt, on extreme averages, dogs being on leashes marginally improves the on-average saftey.
But this 'on-average' is a radical abstraction. What it says is that the dog's freedom, enjoyment, and that of their owner must be Brought Into Order to fit with a system of values which discounts that entirely.
The sign is a symptom of this system of disciplining people; it conscripts them into a value system which may routinely be against their benefit and that of many others.
The sign doesnt tell you this; the sign gives you no critical autonomy to engage with its system of values --- in the way a conversation would.
That is how I diagnose this commenter's issue: his critical faculties are not being triggered. Rather the sign is seen transparently as a command to be followed.
There are no Commands to be Followed. There are only people commanding, and following them is advised only if it is advised.