Begin with the question: what makes the fallopian tube actively move an egg along? Two mechanisms cooperate, smooth muscle peristalsis and the rhythmic sweeping of motile cilia on the tubal epithelium. Any disease that paralyses cilia will therefore cripple tubal transport.
Kartagener's syndrome is the textbook ciliary disease. It belongs to the family of primary ciliary dyskinesias, where a genetic loss of the dynein arms leaves cilia and flagella unable to beat in a coordinated way. The consequences are systemic: nasal and bronchial cilia fail (chronic sinusitis and bronchiectasis), the embryonic nodal cilia fail (situs inversus, found in about half of patients), sperm flagella fail (male infertility), and the tubal cilia fail (female tubal dysmotility with risk of ectopic gestation).
Now test each distractor against this mechanism. Churg-Strauss is an allergic granulomatous vasculitis driven by eosinophils and asthma, with no ciliary involvement. Noonan syndrome is a developmental disorder of the RAS-MAPK pathway producing pulmonary stenosis and webbed neck. Turner syndrome arises from a missing X chromosome and gives streak ovaries and primary amenorrhoea, an ovarian rather than a ciliary problem. None of these three disrupts ciliary beating, so none explains tubal dysmotility.
Only the syndrome of immotile cilia fits a tube that cannot move.
\[\boxed{\text{Kartagener's syndrome}}\]