Here's the thing: the term "broken" often gets applied to people who are somehow out of the norm. In all cases I have tremendous issues with other people using the term to describe anyone. If someone wants to deem themselves "broken", have at it.
Various dictionaries have the following definitions for the term "broken":
Forcibly separated into two or more pieces. Having been violated. Being in a state of disarray. Subdued totally. Humbled. Weakened and infirm, not functioning.
The second problem with broken is that the general feeling seems to be that once something is broken, it's broken forever. And while that may be true of pottery, humans have an incredible capacity for healing. Labeling someone as broken also labels them beyond repair. It is a way for an outsider labeling someone as a victim instead of a survivor.
For those who feel or have felt broken during their lives, I would like to introduce the Japanese term "kintsukuroi". It is the art of repairing broken pottery with gold, silver or platinum. It also means that breakage and repair are not things to be hidden but mark a piece of the thing's history.
And often, if you're very lucky, the thing that was broken and repaired is all the more beautiful for having been broken and repaired.