Mabinogi

First, check the quest info, I'm pretty sure there are annoying requirements for the weaving quest that just serve to waste time. For Deian, choose the start a conversation option when talking to him, and go to the memo tab, campfire skill should be an option. Deian will give you a special book with a yellow symbol, in the options for it, select advanced book reading and keep trying until you are successful. Then use the skill and set a fire, learn the skill in the skill menu.

I think one of the requirements is something dumb like "buy a gathering knife" which doesn't count if you bought one beforehand, or used some other tool to sheer the wool.

You probably didn't equip a gathering knife, you have to equip a gathering knife first, seeing as that's the first step