To be on the right-hand side of the person of power has always been considered preferable to being on the left.
Robert Lacey in 'The Kingdom', his history of Saudi Arabia, tells the story of how the USA, in an attempt to win favour with King Abdulaziz, presented him with a top of the range Ford car - the very first automobile in the newly established Kingdom.
For UK, Churchill was not to be outdone and he presented the Saudi King with a Rolls-Royce with all the fittings. Rolls-Royce at that time had the reputation of being 'the best car in the world'.
Unfortunately for Churchill, the Rolls had the steering wheel on the right. This meant that the King, while being driven anywhere, would have to sit on the left of his chauffeur, and the driver would be in the position of power, on the right of the King.
Long story short, Churchill's Roller was never used and the US were given a head start in the battle to do a deal with Abdulaziz for control of Saudi's oil reserves.