I think an early and overlooked aspect of why Andrew starts liking Neil is simply that Neil is the first person to casually engage with him on his level
Nicky, Aaron, and Kevin love him but they don’t really get him in every day interactions. It’s a lot of “… Ok, whatever you say, Andrew.”
And we know the upperclassmen tend to just outright dislike anything he says or does and uses it as proof of him being heartless and violent
Renee gets the closest because she does get him and goes along with him but they ultimately have very different views of life
Whereas Neil, before he even likes Andrew at all, just matches his energy.
“If I can’t get an answer from you, I’ll get it wherever I can. How about I start with your parents?”
“Good luck,” Neil said, feeling cold all over. “They’re dead.”
“Did you kill them?”
He [Andrew] said it so casually, like he was asking for the time, that Neil could only stare at him for a minute. It was such an unreasonable leap of logic Neil didn’t understand how he even thought to ask it. Then he remembered who he was talking to and asked, “Did you kill yours?”
—
“Neil said. "I'm not afraid of you."
“That's why you're so interesting," Andrew said. "How aggravating."
He sounded amused, not annoyed, so Neil said, "I'll try to be more boring in the future."
“How considerate.”
—
And for a guy who desperately wants connection and has never fully gotten it, it must have been as close to fun as Andrew has getting to bounce back and forth with Neil. He could threaten to saw Neil in half with a rusty blade and Neil will just be like “Hotdog or hamburger style?”