Being right handed and leading with my right hand I used to mount on the right, different people got into different habits though. Racing trainers allow mounting from either side. It is said that because people hold reins with the right hand, mounting on the right would mean holding them with the left therefore the risk of losing control during the switch is high. I always held my reins on the left when mounting, so that one puzzles me. My daughter, FFE member with galops and licence, mounts on the right as she was taught, the owner/trainer who has a lot of awards in the stable's office in his name mounts on the right. The exception, which is hardly relevant to the majority, is mounting with a sword worn on the left. Then there is which hand a waggoner holds his whip which is right for all right handed people.
Then there is the 'fact' that a bit over 90% of the world's roads bear traffic on the right and 10% on the left. The reason given is that right hand traffic predominates across continental landmasses, which are well over 90%, then the majority of island nations drive on the left. However, southern and east Africa are the opposite with nine or ten RHD nations and the majority of islands LHD. But then the Pacific islands are about 50:50 and it is large nations like Australia, New Zealand, Indonesia and Philippines. People have said that that is about being former British colonies, but not all are for instance the last two large island nations never were.
The stories are legion but practice still something other. The fact remains that majority drive on the right of the road. However, as long as this world exists UK RHD people will insist that the majority of the world is wrong. It does continue to make the tenor of this thread really quite absurd since nothing is going to change other than a much repeated point about legal conformity being flaunted not being tolerable but too many people clearly doing it here in France, presumably elsewhere in Europe as well.