Sort the four vasculitides into granuloma-forming and non-granuloma-forming groups, then pick the one that does not fit. A granuloma is a tight cluster of activated epithelioid macrophages, frequently joined by multinucleate giant cells. Three of the listed diseases form them. Wegener's granulomatosis, now called granulomatosis with polyangiitis, is named for the necrotising granulomas it builds in the nose, lungs, and kidneys. Takayasu arteritis attacks the aorta and its main branches with granulomatous inflammation of the vessel wall. Giant cell arteritis, true to its name, studs the temporal and other large arteries with giant cells inside granulomas. That leaves classic polyarteritis nodosa, a disease of medium-sized muscular arteries whose hallmark is transmural fibrinoid necrosis with a mixed acute and chronic infiltrate, but pointedly without granuloma formation. Because PAN is the only member of the group that does not produce granulomas, it is the exception the question is hunting for.
\[\boxed{\text{Polyarteritis nodosa (classic PAN)}}\]