Some say that the parent breeds of the Shih Apso — the Shih Tzu and the Lhasa Apso — are not so much stubborn as, well, a wee bit less than smart. Furthermore, there are those who weigh in that the puppies produced when cross-breeding these two purebred dogs result in something that is even more distinctly not-so-sharp. Regardless of what you may hear, read or be told, these are very cute little companion dogs. They do indeed require a great amount of patience when it comes to training, but they will be happy to never leave your side.
Very early training, constant socialization in sundry environments (walking, dog parks, with friends) and an extremely calm attitude will help a lot in mitigating the possible shyness, aloofness and barking that this hybrid dog is prone to exhibit. All the same, there may remain some hostility toward strangers, but with time and on a case-by-case basis, they may become friendly with those whom you see frequently. It may take some work, but the Shih Apso temperament can be made very appreciable.
It's best to understand that these mixed breed dogs came from purebred dogs whose Far East lineages go back approximately 1,500 years or more. The two parent breeds have a collective history of being nothing more than little personal alarm systems that looked extremely adorable. Otherwise, they did nothing else but be looked after, waited on and heavily protected. While that is certainly not the case today, remnants of that demeanor remain, and it is most likely passed down, in part, to the Shih Apso hybrid.