Believer asks: Why would the authorities have perpetrated the very scenario that they most wanted to prevent?
But skeptic answers: It wasn't the authorities who stole the body of Jesus out of the tomb. It was somebody else; Jesus sympathizers might have done it, fearing if their master were to rise bodily out of the tomb, the authorities would have attacked him on the spot. So the sympathizers stole the body and put it elsewhere, to await its reanimation (his re-enlivening which never came about).
Funny thing, the question seems to say somebody could in fact have robbed the body from the tomb and wants to know why.