Competition

From Zanecorpwiki

There's a common theme in the Japanese samurai/ronin tradition (at least as received in the modern era) in which the character is dedicated to competition. Their goal is to find and defeat or be defeated by the strongest. If it's portrayed as a noble pursuit, it's embodied in the protagonist. If it's an obsession, it's a feature of the antagonist.

The "or be defeated by" part is key. Sasaki Kojirō is conceived to have been content to die by the sword of Miyamoto Musashi. He himself was an awesome swordsman, and to finally se the strength of something even more awesome is a joy to behold.

It's the ultimate dedication to the craft. By the rivalry itself, the craft is made stronger so the "winner" is irrelevant. The craft wins, so each master wins.