What a horribly defeatist attitude!
I agree with 'her house, her rules', but why would you encourage someone to be defeatist and spineless enough to not try to change their parent's mind? The parents have the final say but there's nothing wrong with a child explaining their situation and in some cases educating their parents. Good grief, probably more than half the reptile keepers I know, including myself, were initially told they were not allowed to have reptiles but were spirited enough to talk their parents around. If your parents think it's dangerous you have an opportunity to teach them otherwise. If they think it's cruel you have the opportunity to teach them otherwise. If the child is genuinely just not responsible and the parents are smart they will maintain their stance any that's healthy, but the parents might say the child can have a snake if they demonstrate that they have developed enough responsibility, which is an opportunity for the child to develop as a person.
Imagine how dull and stagnant everyone would be if every time their parents said no to anything they completely gave up on trying until they moved out! If you're passionate about something you'll work towards it. This attitude will continue on in life. If you just limply accept 'no' every time you hear it, you're going to be a very dull, uninteresting person. This is terrible advice for a child.
[doublepost=1576132318,1576131282][/doublepost]
If I had a dollar for every time I'd seen this situation I could buy all the beer and roast peanuts I wanted for at least the next hour. The good news I have for you is that in most cases where the child is keen, the parent comes around, and I can tell you some of the strategies which are most successful.
It probably goes without saying, but incessant nagging and whinging usually isn't productive.
If your parents are generally rational, you can explain that reptiles in captivity are generally much happier, healthier and longer lived than wild reptiles, so it's not actually cruel. This is a genuine fact, but will only be convincing if your parents are rational. Many people are quite irrational and just believe what they want to rather than what the evidence says.
Talking about how passionate you are (without being repetitive and annoying) is likely to help. Just mention that you read a book or did some research or want to see the reptile house at the zoo or have an interest in learning about reptiles or working with them in any way you might be able to. Make sure you do it in a positive way, not a pushy or annoying way (this is important with the entire process, and is also generally a good way to deal with most people most of the time).
If your parents are more emotional than logical, showing them examples of positive interactions between humans and captive reptiles might help. Keep in mind that there are some people who keep animals badly or interact with animals badly and you don't want to expose them to that! (You also don't want to be like that yourself). If you have the opportunity, introduce your parents to adults who are positive and knowledgeable and will be able to help talk your parents around. If your parents think their child doesn't really know what they're talking about, seeing adults who can back you up will be very persuasive. Be careful though, there are some pretty... ummm.... questionable characters in the reptile world who your parents may not like and meeting them could be counterproductive.
Think about what will motivate your parents. You can find examples of people who have become more happy thanks to having pets, and reptiles are very convenient, quiet pets which don't scratch the couch or pee on the carpet. Having an interest in reptiles and invertebrates can spark up the imagination and creativity of a young person which can help in their personal development or pursuit of a career.
Best of luck and feel free to keep us updated with your progress and ask any questions you might have. Definitely let us know if (when!) you're successful