Rich said much of what I would say. I'll add...

How old are you? Do you have a job? If you can't get a traditional sort of job at this time, then look for other ways to earn money...mowing neighbor's lawns, or shoveling snow, raking leaves, babysitting, pet sitting, and other odd jobs. Whatever money you can earn, show your parents that you can save it and budget it. Prove to them that you are not only responsible enough to see to the daily needs of your pets, but also able and willing to take on the financial responsibility for them as well.

Personally, I'm a big softie when it comes to pets...I'd have a zoo if it were only up to me. But my husband is VERY strict about such things and we probably wouldn't have any animals at all if it were only up to him. Fortunately, we balance each other out. It took some work, however, to convince him to allow our daughter to get a snake. Part of that convincing came when she saved up $100 of her own money to help purchase the animal and all the supplies needed to go with it. ......she was ten years old at the time.