Here's a thought, feel free to say no.
But what if Kyle loved Elliot as well? I mean, he told Jacob that he wouldn't let her die when he was first trying to get the codes. Then he didn't threaten Ellie at all, even though it would have gotten him exactly what he wanted. Finally, he tried to kill his brother, which like Elliot pointed out, is the only person he knew knew the codes. Wanted to get him out of the way.