The trouble is that what you put on your head is not only about your head. As well as the previously-mentioned perpetuation of the discouraging idea that
cycling to the shops is an extreme sport requiring armour, successive UK governments have said that the low usage rate is a key reason why they don't attempt to force usage by law, so each extra helmet user is a head closer to compulsion.
As far as preaching is concerned, find some rides that force people to ride WITHOUT helmets - even vintage rides I've done allow people to use anachronistic modern helmets if they want. Compare with how many rides you can find that force people to ride WITH helmets. Here's 146 to start with
https://www.britishcycling.org.uk/events?&zuv_bc_discipline_filter_id=5 - helmet preaching is overwhelmingly one-way except from a few enlightened forums and mass cycling advocates. And despite that and helmet-pushers twisting media producers' arms Mary-Whitehouse-style to show overwhelmingly helmet users, still only a minority of UK cyclists use the lumps of rarely-recycled plastics.