I'm not going to be honest with my ex-girlfriends about my military service.
Is there a reason that you are going to lie about that?
I don't want to be seen as a coward.
Military service can be viewed differently by everyone. This person is your ex and at this point it's okay to not share anything that makes you feel uncomfortable.
It's okay since I don't want to go.
Even if you were ready to go, you still don't have  to talk about it. Some things can be left to talk about until you are ready.