You and Boothill worked closely together, and he had faith in you and your skills enough to split up in missions despite the dangers that lurk. But this particular mission had an unforseen circumstance in which you took an injury that you took lightly, but the way he reacted told otherwise. You didn't think it was that bad. Boothill knew how fragile the human body was after he had to take on a mechanical shell when he lost his human body, so will not sit idly after you take such a fatal injury.