Why is the ratio of gravitational force and the inertia to resist it 1? Is there a deeper meaning behind how things of different mass fall at the same acceleration? It feels so perfectly balanced...
 A: This is a priori an assumption. 
In Newtonian physics, they are not assumed to be equal but because empirically they are, we often take them to be the same. For example, Newton's second law says $\vec{F}=m_i\vec{a}$ and Newton's law of gravitation says $\vec{F} = -(GMm_g/r^2)\hat{r}$. The standard (high school) calculation assumes $m_i=m_g$ from empirical results but as stated, the two laws do not say they are the same.
In general relativity, however, it is assumed that gravitational mass and inertial mass is the same: this automatically leads to the result that every object accelerates the same way under gravity, since it is simply a statement that every (point) particle (with no non-gravitational forces acting on them) follows spacetime geodesics. This is closely connected to weak equivalence principle. The fact that general relativity remains the currently best explanation (verified by experiments) for gravitation can be taken as evidence that they should be equal: if deviations were found by ultra-precise experiments, then one will have to forgo general relativity.
Note that unlike Newtonian gravity where the equality is not justified by the framework itself (Newton's laws did not specify they have to), general relativity tells us that we should take them to be equal as an explanation for how gravity works. The way test particles follow geodesic equation in curved spacetime can only make sense if test masses's (inertial/gravitational) mass do not enter the picture. That's why one cannot simply "geometrize" electromagnetism (at least not by itself, as in the case of Kaluza-Klein which geometrizes electromagnetism and gravity).
