The "why" of a story has less to do with the character's dossier than his or her attitude towards it. E.g., you have character who is a policewoman. Did she always want to be a policewoman, or did she join the force because she wanted to follow in her father's footsteps? Or does she hate one particular kind of crime? If you look closely, you'll find that almost all of the "whys" of a story have to do with a character's wants, needs, or fears. So this exercise is a way of examining (or generating) a character through the lens of his/her desires. (Note: This exercise isn't original to me, but alas, I don't remember who first recommended it. I'm passing it on because it works for me.)

Here's the exercise: write, in at least twelve short sentences, twelve or more things about your character's wants, needs, hates, and fears (no-one said a desire can't be negative). One of them should be a secret.

Note that, as a desire for one thing often implies a hatred of its opposite, you'll be making subtle decisions about a character by how you phrase it. This also means you probably shouldn't write about a slave who both "hates slavery" and "loves freedom," because the one kinda implies the other. But taking a slave who hates slavery and saying that he wants to feel proud of his work is adding some extra depth.

Also, although you might not necessarily post all the details here, see if your character's desires don't also provide insight into their backstory, or provide a plot element that you otherwise wouldn't have thought of.