In the 17th century, many young girls are enlisted for national service and are subjected to weeks of harsh selection processes to weed out muggle before being trained as sorceresses. Of course, some time later, the remaining/surviving sorceresses were decommissioned and replaced by the Amazons.
However, I must clarify to my wide audience, why only certain girls whom are just starting puberty can fly on a broom or twig depends on personal preference and proficiency.
Initially, I thought of using genetic mutations of the X chromosome but that failed miserably. I'm hoping for an answer that could cause a change in neurochemistry as to not only affect emotional states but also grants the user magic, similar to D&D style, after going through the rite of passage(training and trial).
The best answer would be like a scientific paper with as few, or no handwaves. By the way, I already ruled out blood type, testosterone level and diet!
 This is a term coined to celebrate majority of us who is intelligent enough to use the broom appropriately but not intuitive enough to abuse it.