Why is horizontal velocity constant in projectile motion?
Because there is no Force acting on the particle in horizontal direction.
Force is neccessary to change the state of a body, either to bring it in motion from rest, to bring it to rest while it was moving already or to change the velocity of the motion of the particle.
If there is no external force on the particle then its state will not change according to the Law of Inertia. So if it is at rest then it will remain in rest OR if it was moving with some velocity then it will continue to move forever with that constant velocity.
In case of projectile motion the vertical component of particle's velocity changes continuously because of the force acting in vertical direction which is its own weight (
But in the horizontal direction as there is no force acting on the
object ; its horizontal velocity remains constant.