The cousin is sexually abusing her, isn't he?
Why do people jump to this conclusion? I think a lot of people here have huge cases of misandry. Cool it with the sexism people. If the cousin was a woman and your reaction would've been any different please reexamine yourself.
It's got nothing to do with real-life and all to do with having read similar stories. IF this were the first manga I had read I probably wouldn't have thought much about the guy and not bothered to look at the "signs" and thought nothing further about the topic.
But it's not, so like everyone else I feel fairly safe in saying that something's going on with the guy. Maybe it's not sexual abuse, but I'd be surprised if he was just a random normal guy.
This of course also have to do with the old Chekov's Gun idea - you don't bring a gun to the stage unless it's fired at some point. Basically, you don't introduce a character unless he plays some role in the story. It's a yuri manga, and he's male. He's doesn't come across as supportive-best-friend-type, yet he feels too prominent to be just some background character, so that mostly leaves antagonistic roles. Again, abuser fits.
I know that sometimes these reading experiences can really screw you over. I remember reading a scifi story I nearly dropped because it read 95% like a stereotypical-het-bodyguard romance. I could point at all the signs of why it's exactly like one of those in the story and say I was perfectly justified in my exasperation.
But it nonetheless turned out the supposed male love interest was actually gay and married and the entire series turned out so far to be completely free of any romance; something I'd never have expected.
So, yes, authors might deliberately or even involuntarily "mislead" readers like that. Could be everyone is wrong here.
But it's just not the most likely case.