Just to clarify, all the "gathering" skills that are made available to you at level 20, skinning, weaving, stonecutting, prospecting and woodcutting, should be entertained by everyone.
'Cause in the "trade" skills that are made available to you at level 40, alchemy, armour & weapon-crafting, gemcutting and architecture, you will need components gathered from all of the above "gathering" skills.
It isn't the gathering skills at level 20 that make up a "profession", 'cause they produce nothing but raw materials and they cost nothing to take up.
The trade skills at level 40 is in-effect your profession, 'cause you're limited to 2 choices with no chance to alter your decisions. And you make stuff.