The deal humans struck with domesticated animals some thousands of years ago is that they give up their ability to do very well in the wild in order to hang out with us, providing us various types of service and companionship. In return, we humans will replace the natural survival skills they've allowed to atrophy with our own resources and dependability. Since they can't take care of themselves so well anymore, we go ahead and take care of them.
People who take on pets or work animals agree to that deal. You can watch the Animal Planet cop shows to see examples of oxygen waste who don't live up to humanity's part of the bargain, but decent folks buy into it even if they don't necessarily think of it that way.
And then the day comes that you can't take care of them, and the only thing you can give them is an end to their suffering. You can't promise new life. You can't promise to make everything right. You can't promise forever. Even though you know that, and you know it's the right thing to do part of you feels like the lowest traitor who ever lived.
Thanks be to God, Who can promise forever, promise to make everything right and promise new life -- and Who can keep every last one of those promises, too.