Wow. You generally hear of this conversation happening between parents and their child...when the child is much younger. Not 24. Kind of reminds me of an old Arthur episode where he has to convince his parents that he is ready for a puppy. However, Arthur is 8 years old.

It's a complicated situation because you are living under their roof, and their rules. So it seems like you have 2 main options:

1. Continue to live with them and try your best to convince them that you are ready for a dog, and wait for their approval, or
2. Move out and get a dog whenever you want.

You'll just need to weigh the pros and cons of staying at home, and choose whichever is best for you.