Possibly the greatest debate in all vertebrate taxonomy is classifying the turtle. If you were to ask an expert about where turtles belong, well, it will depend upon the expert and which papers this expert has recently read.
That’s because the literature on turtles is definitely divided. Morphological comparison studies, some of which have used rather complex statistical analysis of characters, have generally placed them closer to Lepidosaurs. The most common Lepidosaurs are squamates, which are better known as snakes and lizards, and there is another Lepidosaur order with exactly one species left in it. Rhynchocephalia is this order, and it includes exactly one extant species, the tuatara of New Zealand.
Molecular studies have generally placed the turtles either into or close to Archosaurs. Extant Archosaurs are the crocodilians and birds. All dinosaurs and pterosaurs were also Archosaurs, and birds, which are the only living dinosaurs, are certainly Archosaurs.
One would think that molecular studies would solve this problem, but it really doesn’t. The problem is that turtles evolve quite slowly, and trying to figure out divergence times based upon mutation rates could result in inaccurate conclusions.
So no one really has a way to resolve this conflict.
And if you were to ask me, I would say, well, I don’t know. We have some ideas, but they are in conflict. And we have no way to resolve them at this time.
But that’s science for ya.