because if you release the ball, it's going to fly in outward direction
The other man is thinking from a different frame of reference, and they're disagreeing on terminology.
When you release the ball, it travels in a straight line. This is easily shown by looking at the hammer throwing discipline, which is pretty much the perfect practical experiment to our theoretical discussion.
But the other man says "outward". That is because he is thinking that the circular path (when holding the ball) is the normal path, and the straight path (when releasing the ball) is outside the circle.
But that is not an objective frame. In fact, it's the other way around.
All objects that are not under specific forces travel in a straight line. In order to have an object travel differently, you must apply a force to it. So let's think back to our ball throwing example, but let's start from a straight line situation.
We want to make the ball curve left (and end up in a circular path). So which way do we push on the ball? Left. And because we want the path to be circular, we supply a constant left pressure on the ball (where "left" rotates as the ball rotates).
If you draw this on a diagram, you will see that this "left force" points towards the center.
The black path shows the trajectory of the ball. The red arrows are the direction the ball is traveling in. The blue arrows show you the force that you have to apply in order to makes the ball go round, i.e. "rotating" the red arrow.
The blue arrows point inward. In a better drawn diagram, they'd be pointing to the center of the circle. This means that it is an inward force.
Intuitively, we could learn this by participating in the hammer throw competition. Think about this: when the hammer thrower is spinning around, does he feel like he's performing a pulling or pushing motion?
Pulling. Because the hammer keeps trying to move in a straight line (which eventually gets further away from the thrower). To prevent that from happening, the hammer thrower pulls on the hammer, therefore applying inward force to the hammer.
As an aside, to resolve the "different frame of reference" conflict here:
The inward motion is call the centripetal force. The alleged outward motion is call centrifugal force. You'll find many opinions online that claim centrifugal force doesn't exist. And they're mostly right (though I disagree that we therefore should not talk about it at all).
Centrifugal force is actually the desire for the object to move in a straight line (which is not a force, it is the absence of force). But if you think that the "normal" trajectory is the circular one (like the Navy SEAL in your question does), then this straight line appears to be a deviation from the "normal" trajectory.
Which leads the Navy SEAL to conclude that there must be a force causing this deviation.
But he's got it the wrong way around. The circular path was the deviation, and it was kept alive because of an inward force constantly deviating the normal trajectory. When that inward force stopped, the trajectory stopped being deviated, and therefore took the "normal" path again, i.e. moving in a straight line.
Centrifugal force is a perceived force. It's not real. But because the object wants to move in a straight line and fights going in a circle, the supplier of the inward force feels as if the object is trying to "pull away" from him, which is why he perceives it as a force. But it isn't.