When I was in 9th grade, I learned that Aristotle was responsible for holding back physics for centuries because he said that heavier objects fall faster than lighter objects. Finally, in the 16th century Galileo disproved this theory by dropping two balls of different masses from the Leaning Tower of Pisa showing that they both fell at the same speed.

And when I took physics in 12th grade, I learned that Newton's Law of Gravitation explains the results of Galileo's experiment, showing that the acceleration of an object near the earth's surface is always the same $g=GM/R^2=9.80 m/s^2$, where $G$ is the gravitational constant, $R$ is the distance of the object to the center of the earth, and $M$ is the mass of the earth.

This all seemed to conclusively disprove Aristotle's theory that heavier objects fall faster than lighter objects. However, this line of argument neglects to consider Newton's Third Law, which implies that the falling object forces the earth to move at acceleration proportional to the mass of the falling object. And this will cause the distance between the falling object and the center of the earth to decrease faster for heavier falling objects, implying that the heavier objects do in fact fall faster than lighter objects.

So my question is why was I taught that Aristotle was completely wrong when his prediction seems to be totally in agreement with Newtonian mechanics?

Added: If you don't believe me, just check out the differential equations obtained from Newton's Law of Gravitation:

$MR''=GmM/|R-r|^2$ and $mr''=-GmM/|r-R|^2$,

where $m$ is the mass of the object, $M$ is the mass of the earth, $R$ is the position of the earth, $r$ is the position of the object. Making it simpler, we get:

$R''=Gm/|R-r|^2$ and $r''=-GM/|r-R|^2$.

When $m$ is large, $R''$ is large, implying that $|R'-r'|$ becomes large faster than when $m$ is small, implying that the object will eventually move faster towards the earth when $m$ is large than when $m$ is small.

See a similar question here: <https://physics.stackexchange.com/questions/3534/dont-heavier-objects-actually-fall-faster-because-they-exert-their-own-gravity>