Alanis is referring to this concept of duality. We are never just one singular thing, but that we encompass all emotions and attitudes at all points in life. She juxtaposes this with the concept of a hand in pocket (inactive and disengaged) while the other hand remains active and engaged with the world. The ultimate conclusion she makes is that regardless of the contradicting emotions and actions we make and tell, the world is full of everything good and bad, engaged and disengaged.
Alanis is referring to this concept of duality. We are never just one singular thing, but that we encompass all emotions and attitudes at all points in life. She juxtaposes this with the concept of a hand in pocket (inactive and disengaged) while the other hand remains active and engaged with the world. The ultimate conclusion she makes is that regardless of the contradicting emotions and actions we make and tell, the world is full of everything good and bad, engaged and disengaged.