My kids wanted a pet for a long time, too. They wanted a dog because we can’t have cats due to allergies. But we can’t have a dog because there’s no one home for about ten hours a day. The dog can’t be alone that long. It’s torture for a dog to be alone that long. They can survive, but they will be very unhappy.
Cats, I guess, don’t care. They don’t need company (weird).
We decided to let them get a guinea pig. The pig lived in my daughter’s room for four years until it died of an impacted bowel. She made the decision to have him put down. They haven’t wanted another pet since. Well, they’ve asked for a dog, but not very insistently.
You don’t say how old you are, but parents worry about children making decisions about their pets, and being able to care for them. If your cat gets sick and your mother is away, is there anyone taking care of you? Can you get a cat to the vet?
Will you change the kitty litter every day? Will be able to buy it? What about food?
Parents are generally the fall-back when their kids lose interest in the pet. They stop cleaning up. They forget to put water out. So the parents have to do that. If a parent is away a lot, it gets impossible to back up the kid, even if there is someone else there to watch.
And if both you and your mom are away, arrangements for the cat are not easy to make. So it may be that scheduling will make things too complicated. Your mother presumably knows your maturity level. She knows how well you attend to your homework without prompting. She knows how well you do other chores without prompting. Based on past behavior, she may be reluctant to let you have a pet, knowing that she will have to take care of it.
Find out what her concerns are. Maybe you can meet them. Maybe not. But the first step is to understand her concerns.