Many believe the term stems from the dog-like appearance of the seal, while others claim it is grizzled old sailors. Both of these are correct, nautically speaking, but not when it comes to the pirate.
Pirates, and more particularly, privateers, became known as sea dogs after the astonishing career of Captain Rufus the Flatulent.
Captain Rufus was given his Letter of Marque by Henry VIII, and plied his trade in the English Channel, off the coast of Aquitaine, and wherever Henry was at war. The privateer campaign in Aquitaine was particular successful, and Captain Rufus took many a prize. (Henry always had a hard time getting these out of Rufus’s jaws, but he was easily distracted by the piles of cooked swan that Henry had lying around the castle.)
In fact, the etymology of the term begins in Aquitaine, where French merchantmen sailors would cry, upon seeing Rufus’s standard (a set of crossed bones), “sauve qui peu, c’est le chein du mer!” (Sometimes they would just wet themselves and jump in the ocean without shouting anything.)
This “cheien du mer” cry quickly became anglicized, and is the now-famous, “sea dog.”