Question

Why do inelastic collisions lose energy?

Answer 1

Kinetic energy in inelastic collision is partially converted into internal vibration of molecules and heat.
So the kinetic energy after the collision is smaller than before.

Explanation:

The definition of inelastic collision is such a collision that causes molecules inside the collided objects to vibrate and heat up.
That is a clear loss of kinetic energy, which, after such a collision, is smaller than before by the value equal to the energy of heat produced by a collision.

The total amount of energy (kinetic and heat) remains constant, there is no problem with the Law of Conservation of Energy.