i talk a lot of shizen, especially in a51... rarely do i reveal something that is absolutely how i figure something to be... Pets, and pets passing in something i do take serious and don't BS about...
the way i think is gonna be different than most, and i don't mind. here goes:
we don't 'own' pets. we coexist with them, just like we do people. the way we treat them reveals the way we would treat the world if given the opportunity and less the social constructs that are the sole factor that keeps some people in line. Pets, especially, represent 'experiments' where we can actually observe the entire lifespan and in a short (relative) period. Like anything else on this planet, they and everything else are temporary- it's up to you how you interact with them while they're here. you can offer them a better life than they would have had, or you can make them miserable. You can build a relationship, which all things should enjoy in some way while they're here, or you can ignore them. all the while, you aren't going to stop the cycle of life, and, you are 'practicing' how you interact with those having their own independent experience- and influencing, however slightly, how they move forward in their own interactions after you're absent... you can do it kind, mean, apathetic or with empathy.... you reveal yourself whether you know it or not, and people notice (the most important person noticing ought to be you).
it's in this vane, however uncomfortable, that you gauge how you're helping your child develop.
while the pet is passing, the take away is an evaluation of the relationship- and the most important is if a person is proud of that or not... sad, yeah- it's also an experience we should all have- and often enough to remind us how important relationships are (hopefully). pets, in particular, are a great way of isolating our own God complex- "did i give them a good life, mistakes aside?" life and death is out of our jurisdiction (hopefully), but the value of our interaction is on display when something or someone passes. pets passing is but full contact practice and ought to put those emotionally entwined on notice of what they are or are becoming.