Your friend is confusing force with energy. The ball has the force of gravity acting on it constantly throughout the entire time. While the ball is in the person's hand, it has a force countering gravity on it. When the person tosses the ball, they exert a force greater than gravity on the ball, resulting in the ball now having a velocity, and thus kinetic energy.
Additionally F=ma. Once the ball leaves the person's hand, it's acceleration is constant, and negative, i.e. it is from gravity. For there to still be a force upward, there has to be a positive acceleration but there isn't any positive acceleration, only negative.
As the ball travels upward, friction with the air bleeds away some of the energy into heat. The rest of the energy is turned into potential energy by gravity.
When the ball reaches the top of its trajectory all the energy the person gave it has been transformed into potential energy, except for the tiny portion that became heat due to friction. Then gravity turns that potential energy back into kinetic energy (energy of motion) until the ball hits the ground.