What would a professional pilot (politely) tell that person are the reasons that passenger flights landing and take off in fog is not safe, please?
Given a suitably equipped aircraft, with a trained crew, at an suitable equipped airport with visibility at or above legal minima and with the correct ATC procedures in place on the ground in the air it
is safe.
However in bad visibility the problem is often one of traffic management and flow (as was the case at London yesterday AM). Low visibility ATC procedures require (in most cases) a larger than normal spacing between aircraft flying the approach, and often more spacing between aircraft taxing in or out. The result is a reduction in the arrival rate/departure rate, prolonged airborne holding (inbound) or gate holds (outbound)....And the result of that, on an airport that operates at close to 100% capacity on a good day is that schedules are completely stuffed - at LHR yesterday start up delays were around 90 minutes at one point - that meant for a short haul flight it could have been given a start up time that was coincident with the time it was meant to be leaving it's destination to
return to LHR. Once schedules are shot to that extent the airlines start cancelling services ( especially shorthaul out and back flights) in an attempt to have aircraft in position to pick up the schedule later in the day.
(edited to add: Must type faster..I agree with 'wot the last few wrote

)