Stalactites grow down from the ceiling of a cavern, not up from the floor.
They are formed by the slow dripping of mineral-rich water. As the water evaporates, it leaves behind deposits of minerals, primarily calcium carbonate. Over time, these deposits build up, forming the icicle-like structures we call stalactites.
Stalagmites, on the other hand, grow up from the floor of the cavern as the water drips from the stalactites and hits the ground.