I think I get why she was embarrassed. She has a small tongue (which she has a complex about) and couldn't properly say the word "uni-sex" because of it. She was embarrassed to try and say the word in front of others.
Since this series is ending soon, you guys might like this series. It's basically the same premise. It's called Tonari no Seki-kun. https://mangadex.org/title/5009/tonari-no-seki-kun