Why Study Philosophy?

Plato's Euthydemus provides a pithy answer.

In this passage, Socrates explains the motivation underlying philosophical inquiry to Clinias, a student publicly embarrassed by the contronyms and other such semantic gimmickry by the sophist brothers Euthydemus and Dionysodorus.

Then let us consider what follows: Since we all wish to be happy, and since we appear to become so by using things and using them rightly, and since knowledge was the source of rightness and good fortune, it seems to be necessary that every man should prepare himself by every means to become as wise as possible—or isn’t this the case? (Euthydemus, 282a)

In short, one philosophizes (read: strives to gain wisdom) so that one can rightly identify and apply those things that bring about our flourishing.

Seems like a grounded answer for one accused of having his head in the clouds.