Consider that history has shown that some animals were used in warfare and some were not. Those are the easy to declare as trainable or not. The remaining animals would all be arbitrary.
When you look at real world methods for training war animals, there are animals that obey commands (dogs, horses, elephants) and animals that were pointed at the enemy and let loose (bears, big cats, hornets). DF implements the first method, players implement the second method. There is a lot of room for arbitrary in all this, especially when you add different fantasy elements to this concept.
Thank you for the well thought out points! I don't believe the historic angle is one that I considered.
Training a hornet to do much of anything, much less attack designated foes, would seem unfeasible to me, but I can see them being useful in battle as you imply. Contrastingly, I could imagine a bear being trained to defend an entrance, but calling
specific targets on a confusing battlefield might be somewhat beyond them. And then you have dogs which are much more focused and quite advanced in what you can get them to do. The distinction of what constitutes a war animal is an important one I think, especially when it can refer to so many of the things we have already mentioned.
The point about fantasy elements is well observed as well, dwarf-kind may have some advantages in animal training that we lack.
Maybe it's time to get into raw editing
Apparently the [TRAINABLE] token can be added to creatures mid-playthrough, and speaking from personal experience creature tokens are quite simple to add. Just need to edit the raws in the save folder.