It's probably burned out headlights. Cars have 4 sets of lighting filaments: 2 dipped and 2 high beam. Sometimes these can be combined into a single bulb with 2 filaments per bulb, sometimes these are 2 separate bulbs per side. What makes most sense is that the left side has a working low beam filament and burned out high beam and the right side has a burned out low and working high. When you switch from low to high the light switches sides. Replace the burned out bulbs and you'll probably solve your issue.
The other possibility is that the bulbs are fine but the electrical connections for the left high beam and right low beam are faulty. This could be dirty/corroded connections or something wrong with the wiring.
What I would start with is swapping the bulbs from one side to the other, if the problem follows the bulbs then the bulbs are faulty and should be replaced, if not it's something in the wiring or connections and you should start by cleaning the connections.