The only way to convince your parents to willingly let you do something they are against, is to prove to them that you're responsible and mature enough to take care if it.
Make sure you're putting a ton of effort into school and staying out of trouble. Don't do things to piss them off, or act overly immature when they say no to things. If there is a local breeder, or pet store in your area, maybe talk to your parents about the possibility of part time work or volunteering a few hours a week with them so you can gain experience on working with the animals.
They may not agree to it in the end, but there is a chance they might reward your efforts. Either way, it will benefit you.
Good luck!
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