Basically, they're both just stupid the MC doesn't want people to figure out he's gay (and has been in denial all of his life up until chapter 1), so he wears a ring on his finger to trick people into thinking he's married.
MC also happened to be ML's gay awakening (assuming he didn't know he was gay before their time in the military). ML lowley falls in love with MC because of this, but then MC starts acting really coldly to ML because MC struggles with internalized homophobia at this point because he wants to be "normal" (in society's eyes).
When they meet again for work, ML sees the ring and believes that MC is in a relationship, and MC is kind of dumb and forgets that he has the ring because it's such a regular part of his life.
It's been a while since I've read this, but the whole misunderstanding is that ML thinks MC is in a relationship and MC never tells him that he isn't even as they start sleeping together

Sorry but I’m really confused with the story going and the endless misunderstanding. Please help me understand it.