Why should MC be rising at the point of equilibrium?

Why should MC be rising at the point of equilibrium?
or
Equilibrium is never struck in a situation of falling MC. Why?

Falling MC means that the cost of producing an additional unit of output tends to reduce. In a situation, when price is constant (as under perfect competition) this would mean a situation when the difference between the firm’s TR and TVC tends to increase. This means a situation when firm’s gross profit (TR-TVC) tends to rise. So, this will motivate the producer to produce more. Therefore, equilibrium is never struck in a situation of falling MC.