Starting on the left magneto only - why?
The reasons seems to be that only the left magneto is equipped with an impulse coupling which delays and intensifies the spark during engine starting:

Many opposed reciprocating engines are equipped with an impulse coupling as the auxiliary starting system. An impulse coupling gives one of the magnetos attached to the engine, generally the left, a brief acceleration, that produces an intense spark for starting. This device consists of a cam and flyweight assembly, spring, and a body assembly.
[...]
The impulse coupling has performed two functions: rotating the magneto fast enough to produce a good spark and retarding the timing of the spark during the start cycle. After the engine is started and the magneto reaches a speed at which it furnishes sufficient current, the flyweights in the impulse coupling fly outward due to centrifugal force or rapid rotation. This action prevents the two flyweight coupling members from contact with the stop pin. That makes it a solid unit, returning the magneto to a normal timing position relative to the engine.

(flight-mechanic.com on Impulse Coupling, emphasis mine)
On an aircraft with key operated ignition (where the start position comes after both), the right magneto is grounded while you hold the key in start:

Most airplanes have an impulse coupling on the left mag only. During engine start, the ignition key grounds out the right mag, so only the left mag provides spark. The timing of the spark from the left mag is retarded (later than usual) during engine start so the engine will start easier. Once the ignition key is released from the start position, the timing of the spark is restored to normal, and the right mag starts firing.

(askacfi.com)