The term "budo" is relatively recent one. After the Meiji Restoration of 1868, the martial arts were no longer to be used in combat, but rather to be considered exclusive attainments of the warrior class. "Bujutsu" was replaced by "budo," the implication being that spiritual attainment, not physical victory, was now the goal. When, shortly after, the entire concept of a samurai "class" collapsed, the martial arts were theoretically open to anyone interested.
In the same way, "kenjutsu" (the art of the sword) became "kendo" (the way of the sword) and judo replaced jujitsu. Privilege, however, is not so easily given up. Though, in fact, the sword had not been much used in battle since the beginning of the Tokugawa Period, the cult of the sword continued (right up to World War II), and with it a spiritual glorification of most of the martial arts.
One of the ways to make something mysteriously holy (which is what spiritualization consists of) is to make them arcane, restricted, secret. The art of the sword had a long history of confidentiality, teachings transmitted only to cohorts and the like. When the art of the sword became the way of the sword such secrets proliferated. They eventually became, in essence, a theoretical justification, different from others only in that it was hidden.