They don't rotate, but if you leave recruits to pick their own weapons they'll trade them out whenever they feel like it (or whenever a slightly more valuable weapon is available) unless you designate a specific weapon or type of weapon.
Well, that's the problem. In the military screen, I've set that every dwarf in the Squad uses a "short sword".
It's also possible that you have multiple squads training in the same room and just forgot, but if they're recruits the first seems more likely, once they get to a decent skill level (I think it's "Adequate") they will only pick out weapons that they have skill with, unless none they can use are available.
Dwarves in the military, who have nothing better to do, will sometimes choose to go and train, irrespective of if they're set to train or what ever. They should be doing 'individual drill' in this case.
Actually I've got only two squads: one is the Fortress guard (all equipped with crossbows) and the other one is the aforementioned
All-swordsdwarves squad. In said barracks, only the sword squad is set to train.
Now, the problem is not that there are other dwarves of other squads going to train there. The thing is that in the very Sword Squad I've created myself to have only sword dwarves or simple peasants (which later evolved to, at least, Novice Swordsdwarf), suddenly started having, out of nowhere, macedwarves or even marksdwarves.
Now, that doesn't mean that they were training with maces or crossbows, just that this was their main fighting ability, when previously all dwarves has been, at least, Novice Swordsdwarf.
Later, the militia commander, which I've previously set myself to be a Competent Swordsdwarf (and which I cannot remove from the squad, because the game doesn't allow to remove a commander from a squad that has subordinates) became a Dabbling Dwarf in all fighting abilities.
Since I don't think he's got a downgrade, for whatever reason, I think he might have been replaced by a dwarf with inferior fighting abilities. But I don't know why.
So, what I'm going to do is simply plain start to check periodically on the squad to see if there have been any changes at all. I don't know what else I could do.
Anyway, thanks for the help. If I discover anything else, I'll post it.