For people who say for him to hug her, he actually did try, but stopped himself. Look at the right of page 18, where he opened his arms a bit. Then, look at the 3 bottom panels on page 21: He went to hug her, but stopped himself. He didn't feel like it was the right time, or that he even should. Now, is this the 100% sure-fire milliondollar correct way to approach this situation for Kazuya? No, I don't think there is a "perfect" way to do it. I think it's what he thought was best for Chizuru though. She clearly grabbed onto his shirt, and NOT grabbed around him in a hug. Kazuya interpreted it as Chizuru needing to just grab something close to hold, but not necessarily him to hug.
Remember, this is Kazuya we're talking about here. The dude who get's embarrassed thinking about even talking to a girl. This date was the biggest thing he's done for someone in the manga, imo - which could be debated with the whole movie arc. Again, is it the right choice? I have no clue. Is it the socially-awkward Kazuya's choice? Yep. I'm all for it because this is really realistic if you consider who this is.