My theory on that teacher.
He's a time traveler and he got sent back in time, and in the future he was married to Mika (hence his wife's name). That's why he's really nice to her and she has those little pauses around him. You could say he also keeps the ring as a way to remember his objective or something like that.
Normally this theory would be absurd, but it in this manga where they were even talking to god. At this point this seems like the most chill thing that could be happening.