Aru Akise knew that Yuno Gasai was a liar, a killer, and a danger to the person he loved - Yukiteru Amano. Her best traits were her skill in combat and her strategic mind, but they could also be her most dangerous traits if leveraged against Yuki. Despite Yuki's insistence that Yuno had a sweet, caring side and that she'd risked her life repeatedly to protect his own, Akise had no firsthand experience to support this; to the contrary, his own encounters with her made him believe Yuno was only a threat to Yuki.
When Aru first met Yuno, she'd quickly proven insightful by seeing through his lies and forcing him to reveal his bluff. It was also quickly clear to him that she would take any action to eliminate potential threats to Yuki, such as when she rushed at Hinata and stabbed Mao as soon as their guard was down. Shortly thereafter, Yuno vocalized her desire to abandon everyone else in favor of keeping herself and Yuki alive. Her flippant attitude towards the lives of others rubbed him the wrong way, and it was only exacerbated by the way she put a knife at Hinata's throat at the end of the night. Yuno's little speech there, where she confessed her intention to kill Hinata both as punishment for her actions against Yuki and so that Yuki could never fall for another girl? That brand of crazy had "Yandere" written all over it. Nevertheless, Yuki diffused the situation and got Yuno to back down.
Was her disregard for other human lives enough to endanger Yuki's, however? Of that, Aru was initially uncertain. He was willing to accept that this person was important to Yuki, and that mean leaving her to her own devices for a while. But during that time, he still sought to understand the girl.
However, his attempts to understand her had only made him more confused. So far, he'd determined two things. Firstly, according to DNA evidence, one of the three bodies buried in the backyard of the Gasai household belonged to Yuno herself. Secondly, despite the fact that Yuno and her parents were both proven dead, he'd seen Yuno successfully open a vault at the old Gasai Bank via her retinal scan. There were supposed to be only four people on Earth who could open that vault in such a fashion, and she couldn't possibly be any of them. It was unnerving and befuddling, but regardless of what it meant, Yuno's actions had given Aru more than enough information to draw the obvious conclusion.
The way she abducted Yuki, drugged him, and kept him prisoner in the mountains in the name of "protecting" him was more than enough of a warning. When he added that to the mounting evidence of her own deceit, it seemed clear she was a threat. Her actions both defending and hurting Yuki didn't make a lot of sense when added together except for in one scenario: She was lying to Yuki because she intended to betray him and achieve godhood, and she was keeping him alive only so she could save him for the final kill. Why save him for last? Aru could only speculate. Maybe she just wanted the last kill to be easy. Maybe she just wanted to use him to double-team the rest of the remainder.
Aru knew that Yuno Gasai had to go. Protecting Yuki meant that Yuno had to die — but first, Yuki had to realize just how much of a threat she was. Once she was cleared out of the way, it was a relatively clear path to ensuring Yuki's godhood.
Yuno Gasai knew that Aru Akise was a liar, a manipulator, and a danger to the person she loved - Yukiteru Amano. His best traits were his skill in stealth and his investigative mind, but they could also be his most dangerous traits if leveraged against her Yuki. Despite Yuki's insistence that Akise was a good friend and that he'd risked his life to protect Yuki's own, Yuno remembered nothing to support this; to the contrary, her limited recollection made her believe that Akise was only a threat to Yuki.
When Yuno first met Aru, he'd quickly proven intelligent by manipulating Hinata's assumptions about him possessing a diary into a fighting chance to save Yuki. However, that chance was no more than 50% given that he risked it all on a coin toss, and Yuno didn't take kindly to seeing someone recklessly gamble with Yuki's life. When she considered that Mao and Hinata both threatened to kill Yuki at knifepoint, Aru was willing to leave his survival to random chance, and Kosaka was a selfish jerkass on a good day, it didn't leave her with much concern for the new gang's well-being. By the night's end, Yuki was desperately trying to remain friends with the people who'd endangered him, and Yuno simply couldn't comprehend that. Was he really that lonely, even with her around to keep him company? Or was he already developing feelings for Hinata? Either way, slashing her throat seemed like the best way to preserve both hers and Yuki's future. Yuki, however, had chosen that moment to properly introduce her as his girlfriend - his girlfriend! - and that's when she accepted that Hinata wasn't a threat to Yuki's feelings after all.
Were any of them still a threat to Yuki's life, however? Of that, Yuno was initially uncertain. She was willing to accept that these people were important to Yuki, and that meant leaving them to their own devices for a while. But during that time, she still sought to understand them.
However, her attempts to understand Aru Akise in particular had only left her more confused. The boy had no past. His parents being dead wasn't that weird — the same was true of Yuno, after all — but the way that he had no school records prior to middle school was definitely strange. The property history on his home indicated that it hadn't even been occupied for that long. Yuno wished she had his investigative know-how so she could dig deeper, but those were the only public records she could scrounge up. It was unnerving and befuddling, but regardless of what it meant, Aru's actions had given Yuno more than enough information to draw the obvious conclusion.
The way he showed up with Ninth in the midst of her and Yuki's assault on Eleventh just so he could reveal that the third body in Yuno's yard was her own? That spoke volumes. Here he was, teaming up with another diary user against Yuki and Yuno, trying to drive a wedge between them. And then, when Yuno found Eighth standing in the midst of the Sakurami Tower, it seemed like an easy victory over yet another diary owner... until Aru stepped in to block Yuno's attacks. He explicitly chose to defend another diary user against her and Yuki in a game in which there was only one winner, and there was only one scenario in which that made sense: He'd betrayed Yuki in favor of supporting another diary holder for the role of god.
Yuno knew that Aru Akise had to go. Protecting Yuki meant that Aru had to die — but first, Yuki had to realize just how much of a threat he was. Once he was cleared out of the way, it was a relatively clear path to ensuring Yuki's godhood.