What's with this diamond you mention? No one said it was easy. If it was easy, dwarves would be able to pop out large diamonds all the time. And have you noticed how much longer it takes for a novice to do something?
Um:
Large gems are an exceptional result even in real life, you can't argue that not producing one is a failure when instead you get a handful of smaller flawless gems.
You fail logic forever.
No, I don't. In the game, whether or not you get a large gem is completely based on skill, implying that they all start out large. This is my logic.
If they were like real life, however, smashing a small gem would just get you more small gems, eliminating the possibility of dwarves completely failing to cut them. What you get now is not one small gem; it is a lot of small gems, hence why it refers to those items in plural. I modded in clear plastic as a gem, a small gem item of those are called "clear plastics." Plural.
Oh, and about dwarves knowing how to do something when they grow up:
The craftdwarfship of the dwarves is unparalleled. Let's trade!
The game tells us that dwarves are supposed to be good at this stuff in general. This suggests that it is culturally important to dwarves and children are at least shown crafters at work. Children in forts tend to wander around a lot since they "do as they please," so they probably see this stuff on their own, too. Then you consider that jobs a creature can do are based on its home civilization, not its species. A dwarf raised by kobalds can't be a mechanic.
Oh, and pilsu. A no-quality set of small gems is not a handful of flawless gems.
Finally, @ G-Flex: That has already been suggested, and while it is an interesting idea, no-quality items fill in the role you describe. That's essentially what no-quality means - shoddy. Though I would like it if the overall mood of the fort was unhappy, they would be described as shoddy (pessimism due to hard times), but that's just flavor.