Why is this relationship? Most likely because the child has been pestering the Parents to get a dog at home and parents have refused because either one or both of them don't like the pets at home or the fear of increased responsibility and commitment which reduces there mobility.
The Parents are right to some extent. We have had our pet (dog) second time now. Both times it was our son who picked up the Dog (first time he was hardly 8 years old) with a promise to do all the tasks related to the dog, but the promise was extremely shortlived and the Dog lived fairly reasonably long life.
It obviously meant that the care for the dog became our responsibility from the time they arrived at home. When the second time Dog was taken in, our son had become an adult and hence some days when we forced him, he would take the dog out for a walk or give him Bath.
Let it be clear if you do pick up a pet dog because your son/daughter pesters you and you finally agree, the responsibility of the dog is going to rest with you. Worst still, if your pestering child is either about to finish the education or already working, he/she may just leave for another place but the pet would still be with you. It is important to take a pet (including a dog) only when the whole family agrees to get a pet otherwise don't risk that soul's life by getting him/her at home and then making that pet suffer.
Serious responsibility comes onto you when a pet is brought home. But if responsibility is not a burden, the pet at home is a sheer pleasure. They are the best companions that one can have, a dog in particular. Whether there are people at home or you are alone, the dog keeps the home alive and you have the guaranteed company at all time.
They will be with you. They will force you out of the bed. They will make you play with them and they would be so alert that a footstep outside your door would get an instant response by way of loud Bark. Whether an adult or a child or an elderly, with a pet in general and a dog in particular, would never be alone. For a parent whose child is alone at home but the home has a dog, there would be no worry about the safety of the child and the security of the household. As long as the dog is there, no one would dare to look at your house with a not so good intention.
Even when alone, your day will have activities related to your pet. Feeding the pet, tending to the pet, playing with the pet, enjoying moods and the antics of your pet, particularly dogs, are all fun. They provide essential companionship without demanding much from you except for some love and attention and a little bit of food.
Pets also have therapeutic value. They uplift your mood, they help the Spastic children to improve, they help sick recover faster and there are many such documented research indicating various other therapeutic effects of the pets. Not to forget "Seeing Eye Dogs" who assist blind to navigate (I am not sure if Seeing Eye Dogs are available in India) and in many cases, they have saved lives of the Blind by stopping them from falling into Lift Shaft/ditches.
Having a pet, a living being, in the household does impose some limitations but what ones get in return from that pet is more than the trouble we have to take. If the people of the house have to go out, there are Kennels for dogs (not sure if a similar facility exists for other pets like Cats, Parrots, etc). Recently we did a long trip by boarding our dog, a bundle of Energy called Cookie, in a Kennel.
Therefore, in a reluctant household having a pet is a trouble (actually they are the ones not cared for in such a household) but in a willing household, a pet or pets are definitely not a trouble but a gift of God.
Dedicated to our first pet, a lovely Show Stopper German Shephard, Donna.