Answer: Penetrating injury to the eye.
Step 1: Sympathetic ophthalmia is a rare, bilateral granulomatous uveitis. It is an immune reaction directed against uveal antigens.
Step 2: It needs a triggering event that exposes hidden uveal antigens to the immune system. That trigger is a penetrating (perforating) injury or intraocular surgery to one eye, the exciting eye.
Step 3: After the trigger, the uninjured fellow eye, the sympathising eye, develops the same granulomatous inflammation.
Why not the others: Blunt trauma, chemical injury and urinary tract infection do not breach the globe to expose sequestered uveal antigens, so they are not prerequisites.
Ref: MSD Manuals, Sympathetic Ophthalmia.