Even after watching the movie I was little confused based on the name of the title Peaceful Warrior what exactly it signifies with respect to the movie.
Generally, we assume warriors to be kind of strong and wise military commandos.
In case of Peaceful Warriors, we got warriors who do meditation and aren't worried about things. However, they are still warriors, as the book Way of The Peaceful Warrior and movie say, whether it is Socrates Ninja-ing criminals, Dan performing gymnastics feats, or simply being happy and truly aware of life.
Therefore, this is a different approach to what a warrior is besides what we already know.
When many people think of a 'warrior', they often associate them with a fierce or astrong character. However, the word 'peaceful' strongly contrasts with this, creating the effect of oxymoron. This makes the title an effective one, and gives it deeper meaning.