I peg it down as a sense of duty for all of them:
Duty for someone special (Jake, Tobias and eventually Marco)
Duty for a cause you believe in (Ax)
Or duty to protect something important (Rachel and Cassie)
And on this last point, I associate this to the friendship of the girls, they had a difference sense of how to go about it, but they both place it as this needs to be protected, and we'll do it.
I don't think Rachel jumped in saying "I want kick butt", it was more of, "something's in trouble, and I'm gonna help by kicking butt"
Now Marco, for a start, I'd call it a duty to his friends, but hey, he's a complex guy, I'll never pretend to understand it.