Question

give the reason why the horizontal component of the velocity of a projectile remains the same at every point of its flight

Answer 1

Because ...

-- If you ignore air resistance ... which we always do for these problems ... then there's NO horizontal force acting on the projectile.

-- Since there's no horizontal force on the projectile, its horizontal acceleration is zero.

-- Since the projectile has no horizontal acceleration, the horizontal component of its velocity is constant.