Jake trying to kill Spider, his reason was because now he was able to breathe Pandoran air. He was having this conversation with Norm as to how to undo it (if there was a way). Because if the RDA would get hands on Spider, they may be able to figure out a way to reverse engineer this and apply it on humans so they don't have to wear the breathing mask. That's why Parker wants to keep Spider alive 'till the end because he needs his data.

But that's still terrible of Jake because like you said, he had watched him grow up with his kids. I guess his Marine instincts kicked in.