I am really curious if hair actually tuns white/gray from default color, or does it have a defect as it is made and grows out of your head a different color?
It can actually be for both reasons and it more or less depends on the age what happens. The pigment of the hair is produced by pigment cells (the melanocytes) in the hair bulge and is then integrated into the growing hair (image from here).
The pigment melanin produced by these cells can be destroyed by reactive oxigen species which then leads to grey hair which can still be pigmented at the tip.
The other possibility is connected to the hair cycle. After growing for a while the growth stops, the hair falls out and the hair follicle goes into a resting state. In this phase the pigment cells die. When the hair follicle starts a new hair cycle, the pigment cell population in the hair bulb is renewed from the melanocyte stem cells in the hair bulge. Over time the number of the melanocyte stem cells gets lower until there are none left eventually. At this point new hairs will grow without pigment and be grey/white.
There are two interesting publications about this topic: