The way samurai hold their swords, specifically when drawing or sheathing them, is known as a reverse grip or "tsuka-gashira" grip. There are a few reasons why samurai would hold their swords upside down:

1. Practicality: The reverse grip allows for a quicker and more efficient draw of the sword. By holding the handle with the blade pointing downward, the samurai could grasp the hilt closer to the blade, reducing the distance the hand needed to travel during the draw. This grip enabled faster response times and facilitated swift and fluid movements in combat situations.
2. Improved Maneuverability: Holding the sword in a reverse grip provided better maneuverability, especially in confined spaces or during close-quarters combat. The grip allowed the samurai to manipulate the sword more easily in tight quarters, making it easier to strike, block, or parry with precision and agility.
3. Tactical Advantage: The reverse grip had tactical advantages in certain combat scenarios. By concealing the length and shape of the blade, the samurai could surprise their opponents and maintain an element of surprise during the initial stages of an encounter. Additionally, the reverse grip allowed for versatile slashing and stabbing techniques, as the samurai could transition smoothly between different angles of attack.
4. Cultural Tradition: The reverse grip was part of the samurai's martial arts training and techniques. It was taught as a fundamental aspect of swordsmanship and passed down through generations as part of their fighting style and discipline. The practice became deeply ingrained in samurai culture and was considered an essential skill.

It's important to note that the reverse grip was primarily used during drawing and initial striking actions. Once engaged in combat, the samurai would often adjust their grip to a more traditional grip, with the cutting edge facing upward for better control and leverage during longer engagements.

The reverse grip technique was specific to the samurai and their swordsmanship traditions in feudal Japan. Today, it is primarily studied and practiced in the context of martial arts or historical reenactments rather than as a practical combat technique.