RNA isolation- role of pH
In this case there are two properties that determine the behaviour of RNA:


Its polarity;
Its acidity.


Because of its polarity, RNA tends to escape the phenol-clorophorm phase; actually, it can go into the aqueous phase even if the pH is neutral [1], but with a lower efficiency than if the pH is acidic. Here comes the second property, RNA acidity. Because of that, when RNA is in a neutral solution, it has a negative charge: the $-OH$s of the phosphate group dissociate to $-O^-$ and $H^+$. However, this does not happen in an acidic solution, where there are already too many $H^+$. Thus, at basic pH the $-OH$ groups are intact and have a neutral charge; this stabilizes the system.
Think about it: if the aqueous phase is at neutral pH and fills up with negatively charged RNA molecules, after a while no more negative molecules can enter that solution. On the other hand, if the RNA molecules that enter the aqueous phase stay electrostatically neutral, the number of molecules which go into the solution will be limited only by the availability of water molecules to dissolve them.

That is why you use acidic* pH, it is simply a matter of efficiency.

Disclaimer: This answer is based upon a comment by the OP under the OQ.

[1] You would never use a high-pH solution to extract RNA because such condition hydrolyses RNA.