-Teaching should be buffed a lot. I think a lot of the problem with teaching is that one dwarf that is very bad at learning is taught by a dwarf that is very bad at teaching, while in reality most people are at least somewhat decent at teaching/learning do to growing up as a child (this should hold true even in a feudal-style society).
I agree with this. Teaching seems to be done at an extremely slow pace. I've even made a custom reaction to make everyone into legendary students and teachers, and still it seems to take ages to teach a new recruit anything, even if the teacher is a multi-legendary mighty warrior.
The problem may be that organizing takes a very long time. Soldiers will eventually gain skill in organizing and this does appear to speed up the rate at which they can train new recruits, however there really is no way to train up soldiers with organizing aside from playing musical chairs with the manager noble position, which is tedious busywork.
To train soldiers from recruits to being passable warriors without the use of danger rooms can take a very long time indeed, and if you're playing in a hostile region full of undead, or under siege by many enemy civilizations you might not be able to wait 5 years or so to turn a peasant into a warrior able to hold the line reliably.
If you have a large, well trained military and are occasionally filling in the gaps with new recruits, then its less of an issue, as the new recruits will be surrounded be elites who will keep them mostly safe while they train up as well as get in on the action. Problem is that if you're starting off and not relying on traps or machines to do the fighting for you, its very hard to get a military going without a danger room. Particularly a melee military.