Trauma: The most common cause of a femur shaft fracture in a child is trauma, such as from a fall or a car accident. The presentation of left thigh pain and inability to bear weight following such an event strongly supports this diagnosis.

Osteogenesis Imperfecta: A genetic disorder characterized by brittle bones, which could lead to fractures with minimal trauma. However, this condition typically presents with multiple fractures, blue sclera, and other systemic features.
Low Vitamin D Deficiency: While vitamin D deficiency can lead to softening of the bones (osteomalacia) and increased risk of fractures, it is less likely to cause a acute femur shaft fracture without a history of previous fractures or significant bone pain.

Pathological Fracture due to Bone Tumor: Although rare, a fracture through a bone tumor (such as osteosarcoma or Ewing's sarcoma) can present similarly. Missing this diagnosis could lead to delayed treatment of the underlying malignancy.
Non-accidental Injury (Child Abuse): In cases where the history does not match the severity of the injury, or if there are other signs of abuse, this must be considered to ensure the child's safety.

Carbonic Anhydrase Deficiency: A rare genetic disorder that affects the metabolism of bone and can lead to osteopetrosis (hard but brittle bones) or other bone abnormalities. However, this condition is extremely rare and would not typically be the first consideration in the differential diagnosis of a femur shaft fracture.
Idiopathic Juvenile Osteoporosis: A rare condition characterized by osteoporosis in children without a known cause, which could potentially lead to fractures. However, this diagnosis is rare and would require further investigation to confirm.