This squeamishness is a product of the infantilization western culture seems to be going through recently. Hopefully immigration from 2/3-world countries (e.g. me) helps fix it.
It’s a perfectly legit use of the word. Words are not defined by God; they get their meaning though use, and Merriam-Webster records one such use is “to slaughter wantonly”.
A 'squeamishness' that comes from the reality that we don't need to kill animals to live comfortably anymore. The morality of a rich society is naturally different from the morality of poor country.