Suppose an arrow is flying through the air. Before it can reach its target, it first has to cross at least half the distance between the archer and the target. But after it has reached the midway point, it still has to cross half the remaining distance. And after crossing that, it must cross half of the yet remaining distance. In fact, this process goes on for ever, because the distance between the arrow and its target can always be halved, and the first half always stands between the arrow and its destination.

So, there are infinitely many states the arrow must pass through before it can hit the target, and only a finite amount of time to do it in. The arrow can't possibly do infinitely many things in finite time, and so it can never reach the target. (in fact the same argument, applied to the journey from the bow to any point on its path, shows that any motion at all is impossible for it!)

What's wrong with the argument? If your answer involves adding up infinitely many things, ask yourself how you can do infinitely many things (additions in this case) in finite time---a computer couldn't! What about a bouncing ball? If at every bounce it only reached half as high up as at the last bounce, does it ever completely stop bouncing?