Well Bilbo yes animals die in the end but the keys are as follows

#1 they don't suffer as much...I can't imagine any form of dying not hurting at all but being shot, maybe just in my mind would be a better death than being mauled or being hanged or drowned or being slammed on the ground

#2 Hunting and fishing provides food for people which is a NEED. Dog fighting provides entertainment to a sick few and entertainment is a WANT. Wants you can live without.

#3 You choose the animals you kill and don't kill and humans as the apex preadator in certain areas HAVE to hunt to protect the environment and the species themselves as having too many is just as bad as having too few.