Rabbi Yochanan ben Zakkai said, of the ritual of the red cow, two different things. To non-Jews, he said it was an exorcism. To Jews, he said “It makes no sense, it has no point, but God commands it, so we do it.” (from Midrash Tanhuma).
I read in my Chumash, also, that King Solomon himself labored to understand this ritual, and could not.
I don’t get that. The Torah is full of bizarre rituals, rituals that seem like magic. At the same time the Torah itself, and the Rabbis who followed, are careful to note that the rituals are NOT magic. Their effectiveness stems from God, not from any other forces called into service by the specific actions. It is commanded by God that this is what you do, and so you must do it exactly as God commands. But the fact that you do it precisely is not what makes it work. You do it precisely only because God commands you to do so. That is why the rituals are not magic. But why should the ritual of the brown cow be more mysterious than the others?