Well its a little odd like that. See if your teacher has high skills in something, thats what they'll teach. After a while, when the recruits start to get up in level in the other skills, they'll start doing sword demonstrations.
However, at least from my experience. When trying to get my dwarves to get a solid early weapon skill. The best I've found is to have a squad, with each dwarf equipped with a different weapon. (Usually I train in squads of 5, 1 sword, 1 spear, 1 axe, 1 mace, and 1 hammer) This way, after theya re done with the demonstrations of dodging and such, when the game goes to search for a thing for them to do for training, they'll default to sparring, because they aren't all learning the same weapon. (also it avoids them doing swords demonstrations and such.) After they get up in skill and I start working towards a larger military, I split that squad up into 5 squads training each individual weapon to their squad.
Early on, you might have a few issues, but in long lived forts. After a generation or 2 of masters getting trained by the previous group, their teacher/student skill will be high as well as their weapons/shield etc. New recruits watchign demonstrations from highly skilled teachers grow crazy fast.
Those herpinderpin "cycle your civilians through training so they're all somewhat skilled" things that some players will do, become surprisingly effective at that point because in the few months that they are cycled in to learn, they will actually reach high levels in fighting skills.