The truth is, Jews do not believe in prayer; prayer is a Christian word which means to beg or entreat, implying we are nothing. Prayer would have us throw ourselves before the mercy of the court hoping that the great Judge will change the verdict, effectively changing His mind. But Hashem (G-d) does not change His mind; indeed G-d is as unchanging as He is all knowing.
The Hebrew word for prayer is tefillah which may have an entirely different meaning.
When Joseph comes to visit Yaakov on his deathbed (Genesis 48: 11) he says “Re’oh phanecha lo philalti”, which according to Rashi means ‘I never imagined (or wished) to see your face again’. (Thinking Joseph was dead, Yaakov explains he never imagined he would ever merit to see him again…) Thus the root palel (the same root as le’hitpalel’) means to wish or want….
Indeed, le’hitpalel which takes the reflexive form according to Rav Kook may mean to struggle with what we really want. We are not asking G-d to change; we are struggling with how we can change, which is what Jewish prayer is all about. What we want is really who we are, and Jewish prayer challenges us to struggle with what we really want.