Responses
Uh, no. If you took a proper look, you would see it was Tsukiyama who used his nail to cut his finger, playing it off as a paper cut. Remember the time he and Yomo went to collect a body? His hand wasn't hurt then, and that was before Tsukiyama even knew him.
Hello! I know lots of you are wondering: how in the world did Kaneki get a cut on his hand from a teacup, but not the knife to his stomach? Here's the gist of it.
Kaneki was given the majority of Rize's internal organs, meaning that those organs would have been prevalent in his abdomen and have multiplied the amount of RC Cells (ghoul cells) in that location from the shock and surgery. Thus, when he tried to stab himself with the knife, the RC Cells prevented that, since a ghoul can't be harmed by a normal weapon.
The only way RC Cells can multiply in a body is through injury, and because Kaneki hadn't yet been injured in his hand, he was able to get cut by the teacup because there were no ghoul cells present in that location.
Hope that helps!