You're arguing it from a scientific and not a philosophic point of view.
You think these Greeks knew what a fucking Planck Length was. In fact even from a mathematical point of view the paradox doesn't really hold as it would be what is considered a series and would converge meaning it isn't infinite.
But in reality if you think about it you do in fact meet an infinite number of half-way points while walking a distance, but since you cannot ever reach infinity then movement is in of itself a paradox that cannot be completed.
The point of philosophy is to examine the nature of our world and if it makes you sense and here you are bringing quantum physics into it smh. Just have some fun and think about it.