I wonder if a major difference between humans and other creatures that learn is that humans explicitly teach (repetition with the intention of passing on knowledge to a specified target) while other species just pick things up on their own by observation and reasoning. No idea if those descriptions are true.
TBH, I am not sure the dog does what he does to teach the puppy, rather then to just grab more attention.
Not disputing the overall claim, that animals do teach intentionally.
There is a great podcast by Stephen Fry, he suggests it's because we are able to store knowledge and share it without needing to be in the same place, i.e writing and other forms of documenting culture, that humans have shot so much further in terms of shared intelligence.
Animals share knowledge as well. I think big difference is that we have external storage (writing). Possibly the biggest difference is ability to generate fiction - anyone has idea if some animals are capable of it?