Chihuahuas and Great Danes are not, strictly speaking, subspecies. They are different domestic varieties of Canis familiaris and both belong to the same species. Darwin described species as "well-marked varieties".
If we populate an an island, teeming with game, with 100 male great Danes and 100 female chihuahuas, and come back in 100 years, there won't be any dogs. Ditto if we use 100 f. Danes and 100 m. chihuahuas. If we use 50 m. Danes, 50 f. Danes, 50 m. and 50 f. chihuahuas, then 100 years later we will find two populations that breed true. (We get exactly the same results using horses instead of Danes and donkeys instead of chihuahuas.)
Therefore, the two breeds of dog must be considered different species in some sense.
Since there is a continuum of breeds that can mate with Danes, with smaller breeds, still smaller ones, etc, all the way to chihuahuas, dogs are an example of a ring species.
I never said whether H. sapiens and H. Neanderthalis were capable of interbreeding or not; no one is really sure, or we wouldn't have articles like this.
BTW, the criterion is producing fertile, not merely viable offspring; think of mules.
"Therefore, the two breeds of dog must be considered different species in some sense."
If you took the sperm from a male chihuahua and impregnated a female great dane with it, you would get viable fertile offspring. The difference between the two breeds is one of size interfering with the ability to interbreed, not real breeding incompatability.
"I never said whether H. sapiens and H. Neanderthalis were capable of interbreeding or not; no one is really sure, or we wouldn't have articles like this."
Obviously, one can't be ABSOLUTELY certain. But I'm saying most likely they COULD as they appear from a morphological perspective to be the same species. They look so much alike that there is actually a "continuum" of fossil skulls from manifestly Neaderthal to early modern man. Aside from the skulls, the other different skeletal elements deal mainly with the proportion of bone length, stoutness of bones and size of muscle attachments. There is probably as much morphological different between modern man and Neadnerthals as there is between a Icelander and an Australian Bushman. But not having the flesh and blood specimens in front of us, we can't tell for certain.