Throughout my life, I have never chosen a pet. Sometimes they have been given to the family by someone who could no longer take care of them. One time, my wife chose one from the animal shelter. One of my sons has chosen a couple of pets that sheltered with us in our house (the Cockatiel is still providing mutual support for him). Yet another time, I married into the household which included the cat. Cats, dogs, birds, gerbils, even goldfish -- I didn't choose them.
As I have gotten older, I have gotten somewhat more selfish and have resisted getting another pet. Yes, I would love to have one to cuddle with and have swarm around my legs to watch out for so I don't fall. (I have this specific maneuver that I developed where I turn around in the exact same spot without moving the location of my feet (orientation, yes -- location, no) because, otherwise, I would either trip when changing directions or step on something warm and furry -- 40 years after developing it, I still turn with this method.) But the reality is I enjoy the ability to not have to take care of the pet. To be able to just go somewhere on the spur of the moment. Yes, yes, yes -- I don't actually DO that but I could. But, as one of my blogs was titled, my crystal ball has cracks all through it and I could imagine having some creature entering into my life even if I was not searching for it.
The relationship between a person and their pet is complex and unique for each association. Any pet with whom you actively interact will have a personality (occasionally, even one with whom you do NOT actively interact with, will seem to have a personality -- what, that goldfish ISN'T looking at me?). The pet will also have a history. The cat, chosen by my wife from the local animal shelter, had apparently (only apparent after taking her home) been abused. It took a long time for her to trust us and she was the one for whom I developed my non-dance pirouette. But her purr was memorable and heart-warming and even more so because of the time, and effort, needed to establish the relationship.
At one of the companies for which I worked, well-trained dogs were allowed to accompany their people. Often, at meetings, the dog was the best behaved and most willing to sit and listen to what was said at the meeting. A few years after the company was acquired, dogs were declared unwelcome with that often used, and rarely believed, excuse of "legal liability problems". Speaking for myself -- but probably for others also -- the dogs were missed very much. It is my understanding that many companies are reversing such restrictions as part of an effort to have the office environment be more attractive and supportive. I hope that continues to grow and be more popular. I believe it is beneficial to all.
There seems to be a rise of "therapy pets" -- which is putting a label on an ongoing part of life. To a certain degree, that has always been why we have had pets -- though in some situations they are more work, and life, partners than "pets". Pets become family and, even if they are NOT particularly therapeutic, they remain part of the family. Perhaps the relationship may remind you of others, of the two legged variety, in your family. It is certain that, if you cannot treat a pet properly, it is unlikely you will treat other people properly either. Thus, for other people, such treatment can be an affirmation or a warning about that person.
Legally (though, perhaps, not morally) there is a unidirectional relationship between a pet and a person. But, if they truly become part of your life, it is fully bidirectional and beloved.