For man qua man the possession of white teeth is not a necessary property, evident from the fact that also many (other) animals have white teeth. Whether man qua man is also not necessarily an animal remains to be seen ( A living being, that is an animal, is still not necessarily because of that a man, because there are animals that are not men. But to-be-an-animal could be a necessary condition for something to be a man. I say 'could be', because it is not unthinkable that that something in virtue of which a man is a man can also [evolutionarily] come about out of a totally different material basis, that is, [human nature] being an over-forming of a totally different material substrate ). Man has originated historically from the animal substrate, but that still doesn't mean that this substrate is per se necessary for something to become a man (insofar as he is a man), that is to say that it would be exclusively necessary. On the contrary, other substrates might do just as well. However, it is probable that such an animal substrate is indeed (exclusively) necessary.
From all this we see that the attempt to replace concepts by classes (that is, an exclusively extensional approach) gives problems : the observed relative extensions of concepts, as displayed in Venn diagrams, only suggest, but do not demonstrate, necessity.
This replacement of concepts by classes is called the extensive approach to the study of concepts, in contrast to the intensive approach, as it is followed in Classical Metaphysics (Via Antiqua). In metaphysics the concepts are considered intensionally, and this, because they are intentional : They directly intend something in reality (See VEATCH, H.B., Intentional Logic, 1952, 1970). This presupposes a parallelism between thinking and being, which thesis appears, in general, to be correct. But Classical Metaphysics (not that of VEATCH) takes this yet a step further, by supposing that this parallelism is an isomorphy
( NOTE 218a ), and this latter is, according to me (and to VEATCH) difficult to demonstrate. So any relevant critique should therefore be directed to this supposed isomorphy.