Booster's not very concerned about Barnaby's opinion on the matter, or, really, about the morality issue of killing the Joker in general. They can all have a calm, reasoned debate about it later, when one of the participants isn't in the middle of a messy emotional breakdown.

"Dammit, of course I don't want anybody to die! That's why I'm leaving! I already got my sister killed doing this, and probably my best friend, too, and God only knows who else I've forgotten about! I can't even protect the people closest to me, and you expect me to be responsible for protecting an entire city from one of the worst mass murderers who ever lived? I can't do that! All that'll happen is more people getting killed, and if that happened--if anything happened to you guys, I--I wouldn't be able to live with myself, I couldn't--I coul--I--"

Anything beyond that is lost in sobbing.