When the speed is constant the velocity may not be constant but when the velocity is constant the speed must be constant.why this happens?

This is because speed is a scalar quantity and velocity is a vector quantity. Which means speed only depends on the magnitude at which it travels but velocity depends on the speed at which travel and also the direction to where the object travels.
(Simply whether a body travels to left or right is not considered when calculate speed, but in case of velocity calculation both are different)
So when velocity is constant, it's magnitude and direction is constant. Indirectly the magnitude refers to speed. So when velocity is constant the speed is constant.
But when we say speed is constant we only take it's magnitude under consideration, we will not take care about the direction to which the body travels. So due to the condition that direction may not be constant, we can not say velocity is also constant.
So when velocity is constant, speed is also constant
But when speed is constant, velocity may not be constant (change in direction changes velocity vector)