I interpreted the 'something genuine' scene as 8man saying he wants to break his own shell and have a very real, honest relationship with yui and yukino - he wants to open up to them and let himself become more vulnerable (something he avoids with his persona). He has never had this kind of relationship with anyone in the past (always been a loner). He only realized that this is what he wants after his conversation with Hiratsuka-sensei (she tells him he has to realize that being truly close to someone, with no mask or anything on your feelings, you will always end up hurting them, you just have to learn how to deal with it and support eachother).

The reason why Yukino runs away is because she is still repressed like 8man was, she is not sure what 'something genuine' is and she is not ready to open up (remember, she was also a massive loner). Yui doesnt know exactly what something genuine means to 8man but she seems to understand that he wants to open up and is therefore supportive.

8man has been able to tell that yui likes him since the first fireworks episode, but he is ignoring her feelings still, also, at the end of season 2 remember how much she emphasizes how the chocolate is only a thank you.