When boats first started to use a rudder it was placed on the right side of the boat as most steersmen were right-handed and so needed some room to move.
Consequently, if boats had passed on the left of each other, there would have been a possibility that the rudders would have crashed into each other and been damaged or injure the steersman.
Sorry if this seems pedantic, but is it the tiller, rather than the rudder, that was placed on the right? If the rudder was offset wouldn't that have made steering a little awkward?
The tiller is attached to the rudder. If the vessel has an engine the rudder is in line with the propeller, More than one engine and there is a rudder for each propeller. If the vessel is a sailing vessel the rudder is usually in the centre of the transom (stern) The rudder can be controlled by a tiller, a wheel, or on modern vessels by an electronic joystick.
Nothing to do with boats, but it has always puzzled me that trains in France travel on the left (as in the UK) but the Paris Métro travels on the right. I once asked a Frenchman why, but got the usual Gallic shrug.