So he decided to end either tsukiyama or his girlfriend. Killing tsukiyama's girlfriend is as cruel as killing tsukiyama himselfThink. He threw him off the roof. Had he really wanted to end him, he would've done so easily with his kagune. Ken knew the obsessed Karren would dive in to save him, and between that and imprisonment/death for Shuu, he obviously chose to save him in that particular way.
You can look at it two waysI thought kaneki memory back. Why he tried to end tsukiyama?
She would have died either way. Eto mentioned it.So he decided to end either tsukiyama or his girlfriend. Killing tsukiyama's girlfriend is as cruel as killing tsukiyama himself
It seems more likely
Kaneki: You should fall from here and die quick than to get tortured by me