Of course parents should teach their children to respect animals. That respect should not just extend to companion pet animals such as cats or dogs, but everything else in-between. But we all know that's not the case because people like to play favourites. I've met many people who claim to love all animals, but that love only goes so far as to so called cute and fluffy animals. While the general masses vehemently protest the mistreatment of a puppy or kitten, they wouldn't bat an eyelid if it were a snake or spider. I haven't seen the video but I guess it's probably kids either tormenting a rat or live feeding it to a snake. Depending on the age of the kids they may not have even learned respect yet. It takes time. Some people may never learn it.
A parent's influence isn't enough to shape a child's view of animals. When I was a kid my parents taught me to respect most animals. Unfortunately they were of the mind that a good snake is a dead snake and from a very early age they drummed it into my head, but it would seem to no avail. They didn't mind pythons, in fact, they welcomed them into the sheds. When found, they were something of a novelty and the whole family would come to view them. Venomous snakes on the other hand were to be killed on sight. Oddly enough, both my sister and I don't have this view. My sister's vegan and that explains enough. I'm no vegan but I respect and love them simply because I love reptiles. While I don't have a fondness for rodents I like to think that I treat my breeder rodents well enough. They have food, water, and shelter. When it comes to culling them I do it as quickly and painlessly as possible. Growing up on a farm you tend to have the same view towards animals raised for human consumption. You provide them with all the necessities and when the time comes you put them out as humanely as possible. It's not something I take joy in, nor do I hate it. You're taking a life to nourish another. There's no ceremony to it. I feel good enough knowing that the animals had a relatively stress free life. I don't understand it when people either take glee or offense from it.
Particularly in today's society, most people don't seem to understand the process. They go to the supermarket to buy a piece of steak, or the pet shop to buy pre-killed frozen rodents. They either don't know or don't care that it was once a living, breathing animal. I meet plenty of people who will happily eat a hunk of meat, but they get all squeamish and claim that they could never do the deed itself.