Theres a website dedicated to dogs dying in movies
If youre only argument is, "people are crazy if they get upset over imaginary things happening" then I'm not going to give you the time of the day.
These things cause real emotion to real people. Now I'm not fucking crazy, nor do I need to get a life (as some people have suggested), because I couldn't care less about playing a game that makes me a bit uncomfortable.
There's nothing wrong with hating seeing animals die, even in movies or video games where it's fictional. It's a normal human thing for many of us.
But you're talking about a series with animal encounters and hunting, which has had those things since inception AFAIK. At least since FC2. Now that it's dogs, it's awful.
Dogs can be mean and evil you know.
Obligatory: Cats > Dogs