When In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant while the vertical component of free fall?
In the absence of air resistance there are no forces or components of forces that act horizontally.
A velocity vector can only change if there is acceleration (acceleration is the rate of change of velocity). In order to accelerate a resultant force is required (according to Newton's Second Law,
In the absence of air resistance the only force acting on a projectile in flight is the weight of the object. Weight by definition acts vertically downwards, hence no horizontal component.