Needs education and a change of attitude.
If I'm in a car and can't give a cylist or horse most of a lane width I just slow down until I can - but I'm a cyclist and also wary of horses (they're big!)
I've often been hooted and gestured at for doing this - on one occasion (last year) the brain dead moron behind me managed to frighten the horse with his colonel bogey horn so it threw the rider off (not badly hurt fortunately). The moron overtook, just missed the rider, just missed the horse, and sped off up the road without finding out how the thrown rider was. (Car number noted by another horse rider and passed to the police, but I don't know if they acted).
It's not just cyclists who suffer as a result of stupid motorised drivers, it's pedestrians, horse riders, and anyone else not in a motor vehicle. In the UK the car culture rules.