“Therefore, if what I eat causes my brother or sister to fall into sin, I will never eat meat again, so that I will not cause them to fall” (1 Corinthians 8:13).
In this passage Paul is talking about eating food that had been offered to idols. Jewish converts grew up believing it is idolatry whereas Gentile converts grew up believing it was acceptable. So Paul was trying to reconcile this conflict within the early church. He said it is not idolatry but that if it causes the Jewish converts distress, the loving thing for the Gentile converts to do is to not eat food that was offered to idols (Romans 14:15). Given the word choices used here (meat) and again in Romans, people often cite this issue of idolatry as a parallel to hurting animals and I agree it is applicable. If hurting animals causes a fellow believer distress, you should stop hurting animals or you are no longer acting in love.