If your goal is to cause maximum damage, don't give half-truths, give half THE truth.

One of my favorite plays in social deduction games where one player knows every role/class is to declare to everyone every role they have, but lie about only a couple of them. Everyone else heard theirs accurately, and can confirm with their neighbors that they did too, and assume everyone's information is accurate, leaving the rest of my team to run roughshod freely over the minor purposeful errors.