The Classical Budoka. The full post may be read here.
So the tagai no rei is done throughout a class. It hopefully develops proper respect for each other. You want to train hard, but you want to train with people who respect you enough that they won’t deliberately try to maim or hurt you because they have no regard for you as a human being. They respect you, and you should respect them. Budo is dangerous enough as a physical training system without having to deal with a psychopath as your partner. The tagai no rei ritualizes that respect. For some people, that ritualization may not mean all that much. They may still look at you as merely a punching bag at their disposal, but at least the form of respect tries to embody respect. It’s better than showing no respect at all. And if you find such a fellow student, just avoid the jerk.