The man doesn't necessarily start the dance with his right foot. He can start with whatever foot he chooses to, and in any direction. This is true of all dances.
Many (but not all) Quickstep patterns, however, begin with the man's right foot. That's just the nature of the dance, and how the patterns fit together. The American style syllabus, in contrast, has most (but not all) patterns beginning with the man's left foot. But just because a majority of patterns begin on a particular foot does not mean you need to start the dance on that foot. You can choose to start with one of the minority patterns, or simply start with a prep step.
To someone with an American style background, my advice for starting Quickstep is to first learn the basic
Quarter Turn to Progressive Chasse Combo, thinking of it as the "Quickstep basic". If you start with a "prep step" forward on your left foot (count "slow"), the pattern will feel very much like the Progressive Quarter Turns (aka Junior Walk) from American style Foxtrot.
Regards,
Jonathan Atkinson
www.ballroomdancers.com