The most mysterious master in the grail war is the stoic and serious, although seemingly quite normal Kuzuki Soichiro. A few years ago he appeared at a local temple and took up residence with the local priests. For whatever reason, he then became a school teacher. He's emotionless and very disciplined, yet respected and well liked at the school. Only adding to his mysterious aura is the fact that he's a martial arts master. The technique is remarkable because it utilizes unusual angles, making it difficult to counter without being familiar with it.
Masters are formally chosen by the church to participate in the grail war, although it appears any person can act as a master. Kuzuki had nothing to do with the grail war, but by chance found caster in a weakened state about to pass from the world (having killed her former master and thus having no one to sustain her). Kuzuki takes her in, and ends up forming a contract with her. This is enough to keep her in the grail war, but not enough to allow her to act effectively as a servant. Instead Caster collects energy by siphoning off the life force of people in the town. Kuzuki is aware of this but doesn't seem to care - ironic considering one subject he teaches at school is ethics.
For Kuzuki and Caster, their roles are reversed in the grail war. Caster isn't well suited to fighting other servants, but she's more than a match for any master. Instead Kuzuki's martial arts mastery combined with enhancements from Caster's magic make him powerful enough to take on servants in her stead.
It's unclear why he participates in the grail war since he doesn't have any interest in the grail itself. Is he doing it only for Caster's sake? It's hard to say, although the rumor around school says Kuzuki is going to marry a mysterious woman who appeared at the temple not long ago.