This sounds like any one or more of the equipment issues with the military.
Check if:
A: Woodcutting is enabled at all(Disable it if it is)
B: Mining is enabled at all(Disable it if it is, it doesn't cause nearly the same issues woodcutting will, but etter safe than sorry)
C: The dwarf isn't wearing some weird conflicting civilian clothes(This generally only applies if you are using "over clothing" in the equipment screen, but it could if you equip obviously incorrect stuff, like 5 mail shirts and a breastplate, or leggings and greaves, or gloves and gauntlets, or shoes and boots). Occasionally i'll draft a dwarf wearing something like a robe and a toga and a shirt and he will only equip either a mail shirt OR a breastplate, and he will either freak out and switch back and forth over and over, or stand in the meeting hall screaming "WHAT THE HELL DO I DO?!?!?!?". To fix this, i'd recommend switching him to "Replace clothing" and "Exact Matches" in the equipment screen, make him a dress or robe, and have him wear a dress/robe, mail shirt, and breastplate from body armor. The rest functions normally.
D: The dwarf is set to "Exact Match" and something you told him to equip isn't available. A thief could have stolen it, it could have been accidentally forbidden, could have been accidentally melted down, a woodcutter could have grabbed an axe, a weapon/armor crafter might have been short materials and given a job cancellation notice that got buried under a million Urist McRetard cancels Store Worthless Trash Item in Stockpile: Grizzly Bear Eating Face. To fix this you just need to look at the equipment screen for the militia commander position, if something is missing it won't show a little green mark on the far side. You just need to make something for that slot and they'll grab it and go off to training like the rest of the dwarves.