I am not a dwarf, but I and my dwarves both have hands. Abstraction will be reached further down.
I may not be much of a woodcrafter myself, but I know some things about handywork. I can tell when a bookshelf or dresser was made by a construction worker, instead of a real carpenter, just as you can tell when a house was designed by a carpenter, or a dollhouse by a draftsman. They are uglier, less durable, and generally have defects that reduce their usefulness; Bookshelves will have shelves too close together, drawers will beak easily or constantly get jammed, the bathroom will also be the hallway(I lived in that one), etc. However, I have never seen such an object fail to actually exist.
Upon considering it, one of my earlier statements is incorrect. I have jigsawed some simple toys out of boards before. They were blocky little planes, held together by recessed screws and wood glue, but otherwise quite suitable for giving to orphans (a function they performed). I bought the pegs to hold the little propellers on, so it doesn't really count as making the whole thing, and didn't design it myslef, but the idea is the important thing. None of those five planes were fine, or even decent quality goods, but they weren't failures. I wouldn't give you a dollar for one of them; I doubt they were worth the materials I put into them, on the open market, but since they didn't burst into flames, kill me or crumble into sawdust, their failings were sub-critical.
If I'd had to cut them out with a hand saw, they'd be even blockier, and the sanding would have taken a lot longer (particularly since I have trouble with the whole crosscut/ripsaw thing), but I could've done it. Starting with round blocks would have seriously delayed the project, but again I'd have got at least one of the things done, before christmas.
Oh! I also made a bookend. That nearly did end in failure, though if it had, it would have been me failing to realize how easily the project could be salvaged, and my actual incompetence violating conservation of matter. Though the details of that project make me wonder if dwarves have bow drills or crank drills, since I did need a drill.
Now, I am pretty rural, and I grew up around people sawing up wood and making things out of it, so maybe I'm a biased sample, but I'm pretty sure that I'm one of the least competent carpenters on earth. I have tremendous respect for anyone who does it very well, but no respect for anyone who feels that such skill gives one the right to believe that nobody else can do it at all.
[/compulsive self correction]
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Armor is a special case. On the one hand, chain mail is labor intensive and requires skills and knowledge to do properly. On the other, you're not going to destroy the metal, under anything resembling normal circumstances. The day your first suit of ringmail is issued, should be the saddest day in the life of one unlucky soldier; the rings will be oversized and misshapen, the thing will probably fall apart before he even gets hit and the fit will be nine kinds of wrong, but the thing will get finished given enough fuel and years of mind bending frustration. The right course is probably to melt it down and do better this time. Exactly how much that should be reflected by longer manufacturing times, and how often you should produce -3 holey armor, is a delicate matter. Realistic fuels costs for re-working need to be balanced against player frustration, which needs to be balanced against the player's ability to actually upgrade his dwarves into useful craftsmen.
For materials that are being physically broken and cut, to shape them, the issue get's grayer. Can a dwarf be so bad that he can't make a chair out of a load of wood? That's hard to answer, not knowing what tools he has at his disposal, or how dwarven chairs are structured. You can just take a log with two flat ends and call it a stool, but for that you need a saw, and our dwarves are presently making chairs by karate chopping (I know that isn't what it's called!) and pegging together wood chunks of unknown size.
Somebody invented all those techniques and tools the first time, and if some caveman (I know; it's funny. Shut up.) can do it, so can my dwarves. Whether they should be able to do it in four years instead of hundreds is debatable, but presumably your smith wannabe has seen a hammer before, so you aren't starting from scratch.