YuNg ~ Nice photo in your avatar.
I think hair's growth rate is genetic and has nothing to do with its "coarseness." Here's why:
<ul type="square"> [*]"Coarse" has to do with the diameter, i.e., thickness, of an individual strand of hair - not whether the strand is tightly coiled, soft, hard, etc. Coarseness has nothing to do with softness/roughness. It's possible to have soft, coarse hair - or hard, fine hair. Coarseness and the degree of softness, as far as I know, do not affect how quickly one's hair grows out of one's scalp. I believe genetics, diet, and handling do.
[*]Coarseness does not dictate the ultimate length hair length, nor how many strands one has. For example, naturally-straight Asian hair is coarse but can grow very, very long - but all Asians don't share the exact same hair growth rate. One can have coarse, slow-growing hair that is pampered enough to reach, say, waist-length while someone else can have fine, fast-growing hair that breaks off quickly due to bad habits and never even reaches shoulder or nape length.
[*]In addition, it's possible to have many densely packed hair strands that are fine, which makes hair look thick, or coarse hair that's relatively sparse. The reverse is also true. Neither, I believe, impacts the growth rate or achievable length. As Adrienne's signature says, "It's not what you make, it's what you keep."
[*]Coarseness also has nothing to do with the degree of curl/coil/wave. Many black hair care experts describe tightly-coiled (Ben Wallace, Kobe Bryant) and curly (Rick Fox) hair as *fine* - meaning again, the diameter of the hair strand. The coil/curl affects the *appearance* of length - but it doesn't dictate the growth rate and it doesn't have to determine a person's ultimate hair length - as many inspiring LHCF pix show.
[*]In my humble opinion, genetics determines one's growth rate, how much hair one grows (sparse/thick), or whether one will grow any hair at all. Diet, handling (eg, chemical abuse, too tight braids, improper weaves, etc.) and physical health also directly hair growth rate. Retaining length is a related, but separate, issue.[/list]
Hope that made sense!