It is called mathematics. All I am saying is that the statements:
1. the first law of motion defining inertial frames of reference is true and
2. all intertial frames of reference are equivalent is true.
imply that F = ma.
In my example where I add unit pulls and the same number of unit bodies, if a = (iF)^2/iM = i(constant) then the relationship between Δv and Δt would not be linear. It would be proportional to the number of unit forces or unit bodies that I have added.
The result would be that I can increase the change in velocity of a unit body per unit of time by i+1 times simply by being in the reference frame of i other non-interacting unit bodies each being independently pulled by the same unit of force. The conclusion would be that the change in velocity where the same pull is applied to the same body for the same period of time is not the same in all inertial reference frames, which negates the premise.