Stalactites and stalagmites are usually made up of the mineral calcite. This mineral dissolves easily in acidic water. How do you think calcite hardened to form the features in the cave?

In caves where water doesn’t flow the stalactites and stalagmites form. So the Calcite is saved from being dissolved.
Stalactites:
When water carrying soluble minerals fall drop by drop from the roof of the caves some minerals still remain there hanging from the ceiling of the cave the minerals crystallise there when the water evaporates and it forms Stalactite. The word C stands for ceiling.
Stalagmites:
When water carrying soluble minerals fall drop by drop from the roof of the caves the minerals in the form of solution also fall on the ground of the cave. After the water gets evaporated only the mineral remains there to form Stalagmite. The word G stands for Ground.
Inside the caves usually running water is not found. thus the calcite deposit is not washed away and the Stalactites and Stalagmites continue to grow.
but in those parts where flowing water washes away the Soluble mineral deposits stalagmites are not found.