I understand why Kiara is putting her foot down on the shipping thing. It's possible that the idea was just thought up by management and wasn't based on their actual personalities matching.
I think it's also because it's ruined her reputation a bit. She mentioned on a stream a while back that she was confused why the fan base thought she was a nymphomaniac. She flirts just as much as the rest hololive, and makes less dirty jokes than Ame, Gura, Coco, and Hachama. But she was still "The horny one" just because she was the first to flirt.
Probably screwed up her actual friendship with Calli, too. She couldn't collab with her or interact with her in a game without people expecting her to make a scene with the same tired old jokes. No one could blame them if they tried to avoid each other because of how annoying the pressure to act unnaturally would be.
It is a little unclear how much of it is actually just her being weirded out about faking a relationship with someone who she knows a lot better. It's interesting to hear that Kiara wasn't that close to Gura for a long while, and is pretty close to Ame. I really didn't get that impression. Makes me wonder if she really saw Calli as a close friend at all, or if she was just acting what was expected of her. That's just speculation, though.