There is nothing wrong with assuming something that is false. Doing so and coming to a contradiction is a common way of disproving the premise. Also, you misse

There is nothing wrong with assuming something that is false. Doing so and coming to a contradiction is a common way of disproving the premise. Also, you missed the point. The premise is that heavier weights fall faster. The cleverness in the argument rests in consider what happens when you break a heavy rock into two differently-sized pieces. Using the premise each should fall slower than the whole; but what changed? Do they somehow know that they are separated? Of course not, that's nonsense. There is no "knowing" if they are one object or two. Therefore everything falls at the same rate. Which is true assuming no atmosphere. The argument is still valid in the presence of an atmosphere, all you have to do is ensure similar drag coefficients.