@Maya500 Hosts are free to offer any discounts they please to guests, but military/government discounts are not a thing on Airbnb at all. Military people know this, so your suspicions that your guest might not be legit are completely valid (thousands of people try scams on Airbnb every day). I would never offer a discount upfront on request - it's usually a red flag - but instead I might surprise the guest with a thoughtful gift or a rebate at the end of the stay, if everything goes well.
If the person does not want to book your home without the military discount, that's a good sign that you've dodged a....oh, never mind.