I think people are taking too seriously what is supposed to be a gag. Mai is a child, Mai looks like an adult, Mai is unintentionally saying or doing something that flusters Tae.That's pretty much it.
It was really cute. I think it's the first time Mai addressed her looks. I hadn't thought of it before, but It must be hard for her, since she's so young, she must get a lot of comments from both other kids and adults.
Chikako is probably bullied because her family has an inugami. Considering that it's out in the open, I wonder if the setting is a school for supernatural beings? Or is Inukami invisible to humans and Taki's identity is a secret?