Which do you think are better for beginners and kids? The cost, maintenance, handling etc.
Perhaps your mom is looking at it like, "First you got a leopard gecko, now you want a snake, in 6 months you'll want xxx, and then...and then...and then...
So maybe it will just take some time to show her that your interest in the gecko is not going away just because you want a snake. Convincing your dad might be a lot harder. Some people really do have bad phobias. Can you convince your dad that your snake would be safely enclosed in a tank, and that you would only handle it in your room with the door closed, so that there is NO CHANCE of escape? Show him photos of the tank you would buy - including lock mechanism!, and that you will save up the money for all supplies ahead of time, that you are caring for your gecko properly and plan to continue to do so.
Parents also worry about what happens when their kid gets a pet and then they get to be teenagers and have other interests (like dating, etc.) that take up their time other than pets. Your pets would have a long lifespan. Your parents want to know they will not be taking care of it at the other end of its life.
It may take some time. Do be considerate of their feelings, and above all, DON'T NAG OR ARGUE! You can present your wishes, and if they are turned down, ask if you can discuss it again in three months, so that they can see you are serious but are not being a "whiny little kid". Parents always want their kids to grow up to be responsible. It sounds like you are well on your way to that, now just to keep showing them. Good luck!