Well, it's a morality issue really.
Animals are neither inherently good or evil, so killing them simply because they defend their homes is cruel.
Whereas humans can (and in this game) have made an ethical decision to be evil, so they deserve whatever consequences that choice has brought upon them.
Which was the whole lynchpin of that campaign to include the tranq gun.
But there was an interesting variation of this that went unnoticed in Tomb Raider 6.
Lara is on the run from the authorities because she's been framed for murder. When facing normal police and guards, her unarmed knockout move changes.
Because these people are not her enemies, she pushes them to the ground and punches them out, leaving them alive.
But when she does the same move on those who are actively working for her enemies, she breaks their neck.
So, it would appear that Lara is not a psychotic killer, more a practical person. If it is appropriate to let her enemies live, she does.
There have been occassions in the past where Lara (covered in Tomb Raider 5 and 7) has had her enemies completely at her mercy and let them live, although with a stern warning they would not be so luckly the next time they opposed her. Sadly, they did not take this warning seriously and you can guess what happened to them next........