Here u and v are leaves in DFS tree. But u and v have degree >=2 in the original graph.
So now if u or v connects to some unvisited node in the graph, they wont be leaves in the DFS tree, so to have degree>=2 they should be connected to already some visited nodes, and hence u and v both will form cycle with their neighbors. But it is not necessary that they both are contained in the same cycle.