Sure, and a lion being alive results in a “massive loss of life” as well, so long as you consider a single animal’s influence to be “massive,” but that doesn’t mean we kill them. People don’t want to kill things because they don’t want to do it themselves, not because they specifically want to limit total deaths. Not saying it’s better, but it’s still an option, and it’s still better to let the people who don’t want to kill them neuter them instead, rather than not helping at all.