There are two that really bug me:
Variants on this:
'Dr. David Mech, the wolf expert and senior scientist who was largely responsible for the original study promoting "pack theory" now explains that there are pronounced behavioral differences between captive wolves like those used in the study and wolves in the wild...In a natural pack, harmony is created because deference behaviors are offered freely by the younger wolves rather than being forced onto them by their parents. '
(from Victoria Stillwell's website)
Firstly, the original study (on captive wolves) wasn't by David Mech (it was Rudolf Schenkel, 1947). Secondly, David Mech 100% continues to state that dominance is a key element in how wolf packs operate: 'They [the parents] dominate the offspring, they are dominant to the offspring. My only concern was calling them alpha which implies that they fought to get their position.' (Training Without Conflict podcast 33, 16:15ff).
Secondly, not all wolf packs follow the basic model of parents and offspring. Research in Yellowstone National Park has shown that some packs contain two or three breeding females, and that dominance contests within the pack can end in the death of one of the parties (see YNP wolf report, 2000 - alpha female killed by pack mates). Sometimes a lead female will mate with not only the lead male, but with another male as well (YNP wolf report, 2005). Subordinate females might mate outside the pack - appearing to be on their way to forming a new pack - but return to their natal pack to den (YNP wolf report, 2003). Wolf behaviour is extremely complex and flexible.
Sure, wolves are not dogs, but to appeal to wolf behaviour to 'debunk' hierarchical behaviour in dogs is ridiculous. And plenty of scientists and ethologists with expertise in canine behaviour 100% believe that dogs use dominance on each other (e.g. James Serpell, Roger Abrantes). To acknowledge all of that is to say nothing about how people ought to train their dogs, especially as much of dominance is behaviour is carried out not via any sort of overt aggression, but via subtle forms of posturing.
The second one is variants on this:
'Today’s domestic dog is about as genetically similar to the wolf as humans are to chimpanzees.' (Victoria Stillwell again, but the APDT comes out with something almost identical.)
This is legit bullshit. Dogs and wolves split maybe 50,000 years ago (possibly as long ago as 100,000). Sounds a long time, right? But humans and chimps split 6.5million years ago. Humans and chimps cannot interbreed, whereas hybridisation between wolves and dogs continues to the present day (and not always with human intervention, either), and produces fertile offspring. The black coat seen in some wolves came from hybridisation with dogs. Dogs and wolves share >99% of their genome; humans and chimps share 96-97%. Humans and chimps are seen as distinct species, whereas the dog is classified by mammalogists as a subspecies of the wolf. Admittedly its evolution away from the wolf template has been sped up by selective breeding, but still, dogs are much, much closer to wolves than humans are to chimps.
Again, this says nothing about how a dog should be trained. But it doesn't help anybody's argument to underpin it with these claims when they are manifestly not true.