beta
Slight spoiler
From future chapters it looks like the doctor is male. Could it be that Shizuma knows this already, hence he doesn't realize how Minato considers the doctor a "threat"? To Minato, every pretty female around Shizuma is a huge problem, and if he thinks the doctor is a woman (which he does) of course he has a different take on the situation than Shizuma does. Not excusing Shizuma here, the whole "oh he's so jealous when he's cute" is honestly pretty random and kinda inappropriate.
Overall, I wish the doctor didn't play such a huge role, they just seem weirdly involved for no good reason outside of drama.