By monophyletic cladists mean that all of the members of a single group must have a common ancestor. The diagram on the left shows a case of polyphyly. The diagram on the left shows a case of paraphyly. One group of equivalent rank cannot be contained within another according to the rules of phylogenetic systematics. Paraphyly is a common problem in older classification.
Birds represent a classic example of paraphyly.
Birds have always been given their own class, Aves. Birds, most people agree, however are derived dinosaurs. The solutions are to either do away with Aves as a class and make them part of the Dinosauria, or to raise all of the dinosaur groups to class level. There is a third solution. Ignore the problem.