Why be a bitch?

That must be a coworker of her, if he found out that's she's being visiting host clubs it won't be good for her reputation, that's why she did that. Or else the black haired guy may say something wrong. She was being rude but I can understand why she act the way she did

It's not that I don't understand the situation, but how would he have known that? As far is he knew his job wasn't something to be ashamed of and yeah he was originally a penguin so of course he doesn't understand but there are probably plenty of hosts that don't find their jobs to be shameful at all so they would think nothing of it as well. She didn't have to reach like that a simple "Sorry I'm busy with work and don't have time to talk" would have been enough them message him and let him know to only talk to you at the club. He has no way of knowing that she was ashamed she goes to host clubs so why treat him as if he should have known?

This is probably a cultural divide, where it confuses you. In Japan, there's nightlife places like host clubs, and they're supposed to be more on the low and secret. It's a Japanese way of life, understanding these separations, so him breaking that barrier and talking to her outside of her nightlife is exposing and could be troublesome. She obviously doesn't know he's actually a penguin, and he seems to be somewhat of an expert in hosting, so she wouldn't assume he wouldn't be in the know on customer privacy.