Your dad is right. It depends if the moving object was at rest or moving or accelerating/decelerating when the object is thrown. Usually on Earth you'll be accelerating and moving so slowly that almost any force applied to an object in throwing it will make it fall behind the initial point where it is thrown, simply because you'll need much, much less force to accelerate a ball to an equal or greater acceleration than it takes a bus to get there.
It's actually easer to think about this with a rocket in space, it deals with all the complications of air resistance and comparatively slow velocities. Imagine that I have a two stage space ship in orbit travelling at 2,000m/s. I want to jettison the first stage so I can activate the engine on the second stage. I activate the explosive bolts which, for a split second provide 1,000m/s^2 acceleration in the opposite direction to the direction of travel. The first stage feels that for 0.01 of a second, meaning that I have slowed the first stage by 10m/s. The first stage is still travelling forwards at 1,990m/s.