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...
GOLDEN TIME VIIIIIIIBES. This is what banri was like, cutting out the new one so the old one can be with the one he likes. But in this situation the amnesiac MC is trying to cuck his previous self.
OH WOOOOOW NOW we got the male version of Minori, gonna try and steal Umi. He's gonna invite her out then her airheaded ass is gonna nonchalantly smile and say "OK" then that..... THAT'S when his inner manwhore will show and he's gonna try some sneaky shit.
FUCK YOU BITCH. She's in love with him, she just doesn't know what romantic love is or how it feels so she can't properly determine whether she likes him that way. But you can definitely tell she LOVES him by the way she describes how she feels when she's around him. SO BACK OF BIATCH!!!
OR...
Oh shit, this bitch got him good. So she must be doing the dungeon shit aswell. Also this man's is straight pimpn, tryna have sex with 2 girls at once that he just now started talking to THAT DAY.
Ok so basically this manhua is Chinese Rising of the shield hero. Then, we got all those reference's to basically the most mainstream manga/anime out there.
Hmm I wonder if some shit went down and she had a specific reason for trying to go out with the kubarashi dude. Maybe it was some time travel related stuff, or she legitimately NTR'd the MC. I really hope it was the first one but I don't see how that would work.