It might help to look at your question from a different perspective. You ask why a molecule would prefer to have 0 net charge. Instead, let's consider the impact of having a formal charge. Charges interact, where opposites charges attract and like charges repel. Neutral particles exhibit no Coulombic attraction or repulsion. So in that sense, we can start by saying that charges result in interactions, which in turn means higher reactivity. In general, charged molecules are more reactive than neutral molecules, which by definition makes charged molecules less stable. For instance, this is why we consider RS- to be a better nucleophile than RSH, because it has a negative charge making it a more reactive Lewis base.
Beyond the actual charge we also have to consider stable electronic arrangements for valence electrons. VSEPR theory coupled with valence shell theory support the notion that second row elements are most stable when they have a complete octet (8 electrons distributed into four pairs.) We look at the periodic table for confirmation, but the hard truth is that we don't know why it does this, we just know that it DOES do this. So our observation of millions of examples becomes our rule to follow.
Combining your two questions we find that a molecule has two driving forces for stability: (1) to have no formal charges on any atoms if possible and (2) have every element with a satisfied valence shell. For some elements, like boron, it is not possible to achieve both. If boron takes on a fourth bond (to complete its octet), then it takes on a formal charge of -1 and thereby becomes more reactive. This is why borohydride (BH4-) is such a great reducing agent. If it only has three bonds, and thus is two electrons short of an octet despite having no formal charge, it is a strong Lewis acid, such as we see in BF3.
Your question is an excellent 'meaning of life' question that is at the root of our theories in chemical reactivity. Try to see the big picture, knowing that there will be exceptions (there always are), and keep things simple when looking at MCAT questions. Try to follow the two rules above when deciding if a molecule will be stable, or how reactive it may be, as the question you're doing requires.
