It seems intuitive that $a\; \propto \frac{F}{m}$, as the greater the force that is applied on an object, the greater its acceleration will be. Inversely, the greater the mass of the object, the slower the acceleration will be.
However, when rewriting proportions as equations, you must introduce a constant of proportionality, and in this case of a direct proportion, if $a \propto \frac{F}{m}$ then when rewriting as an equation you will have $$a = k\cdot\frac{F}{m}$$
In order to get the standard formula $F = ma$ this constant must be $1$. However, how do we know that this is the case? How do we know that the constant isn't $2$ and the formula $F = \frac{1}{2}ma$, for instance?
Answer
I think it is more intuitive to say that (net) force is proportional to acceleration: $F\propto a$. The proportional constant tells us now how easy it is to accelerate an object with a certain force. This proportional constant is called the (inert) mass of said object. Hence $F=m\cdot a$.
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