One of the most famous and heart-breaking moments in the Odyssey is about Argos the dog, who has waited 20 years for his old master and is lying neglected, in the dung. He hears O's voice again, pricks up his ears, and then dies.
Unlike all the humans in the household, who struggle to see through Odysseus' goddess-given disguise as an old beggar, the dog knows his master right away; no need for words or signs or stories. He passes the test without even trying.
One effect of the Argos scene is to show what bad shape the household is in: this great, useful dog is being wasted & neglected. The scene also marks the passage of time. O. is trying to turn back time, to get back to 20 years ago, and maybe he can do it; but his dog can't.
The scene is embedded in a conversation between Eumaeus, the idealized human slave, and O., his disguised master. E. says that it's the slaves' fault that the dog is neglected. He doesn't blame Telemachus, who isn't man enough to take the dog for a walk.
Implicitly, there's a contrast between the bad human slaves, who can switch allegiance or fail to obey, and the dog, who is more purely a living instrument of his master's will. The dog defines absolute loyalty and absolutely abject love of the owner. The best possible slave.
Loeb translation acknowledges this is about slavery:
Slaves, when their masters cease to direct them, no longer wish to do their work properly, for Zeus whose voice is borne afar, takes away half his worth from a man when the day of slavery comes upon him.
And serving men, when their masters are no longer about, to make them
work, are no longer willing to do their rightful duties.
For Zeus of the wide brows takes away one half of the virtue
from a man, once the day of slavery closes upon him.
All the translations, except mine and the Loeb, muddy the waters on the slaves' wishes. The verb is "ethelousin": they don't want. Unlike dogs, humans slaves often don't want to obey. Contrast the "zest" of Fagles, or the "will" of Fitz., or Lombardo's omission of desire.
Poor dog. It's a tear-jerking passage, and it makes me want to cry for Argos, even on the umpteenth re-reading. But it also makes me want to cry for the human slaves: the humans deprived of human "value" (arete), and of agency: turned partly, unsuccessfully, into dogs.
Time changes everything. Anticleia is dead. Laertes is old and broken. Dog dies. Penelope is older, marked by 20 years of crying. Telemachus is growing up. Pigs are eaten & born. E. builds a new hut. Athena can partly turn back time, but only for one man.
I didn't mean to imply anything species-ist. This scene, imho, defines the dog as better at loyalty than the humans. We then have the further question of whether absolute loyalty is always a good thing for humans. Dogs and people might be equal but different.