You first denied that things define a person and then said that they do....
No. It is not one or the other. Think about it for awhile. Things may be the fruit, the evidence, of a person’s freedom. That is not the same thing as defining WHY they choose what they chose or why they do what they do or who they intrinsically are.
I would define myself based on my Christianity, on my beliefs, on my family, etc... and nothing else. But my liberty is evidenced in the entire array of choices that I make, including my property. If my property can be taken by force, then some of my personal liberty has been taken by force.