There are ahadith that clearly contradict the claim about not drawing closer to Allah through abstention from killing animals (presumably to eat them), even in the absence of a different context and animal farming practices:
Mu’awiya ibn Qurra reported that his father said, “A man said, ‘Messenger of Allah, I was going to slaughter a sheep and then I felt sorry for it (or ‘sorry for the sheep I was going to slaughter’).’ He said twice, ‘Since you showed mercy to the sheep, Allah will show mercy to you.’”(Sahih Al Albani, Al-Adab Al-Mufrad 373)
Narrated Abdullah ibn Amr ibn al-‘As:
The Prophet ﷺ said: The Compassionate One has mercy on those who are merciful. If you show mercy to those who are on the earth, He Who is in the heaven will show mercy to you.(Sahih Al Albani, Sunan Abi Dawud 4941)
Clearly, even when animals are raised and slaughtered according to strict Islamic guidelines, abstaining from such slaughter out of mercy is a morally praiseworthy act, and a Prophetically-approved means of getting closer to the mercy of Allah.