Hello! I have two crested geckos and I can tell you now that your mother's estimate of lifespan is even too low. They aren't sure how long crested geckos can live for, as they were thought to be extinct until they were re-discovered back in 1996. Geckos born that year are still going strong and that is 23 years plus. They may even live to be 30-40 or longer! So they are definitely a lifetime commitment.
May I ask, how old are you?
Pets are great, and crested geckos are great as well, so if you're willing to commit to your pet for as long as it takes, then they can be an awesome companion! The best thing you can do is look forward at least 20 years and think about where you think your life will take you. Will you be going to college? Will the dorms allow pets or will your family be willing to take care of your gecko? Will you be traveling often? Crested geckos require daily misting and feeding so they don't work well with someone who travels a lot, snakes are better for that. (unless you're willing to pay a pet sitter :) ), Are you able to take care of your pet once you get married? Have kids? Can you afford the proper caging, supplies, plants, lights and food required for gecko care?
Don't get me wrong, like I said, crested geckos are awesome pets but I'm sure your mom just wants to wait until you are a bit older to guarantee that you are willing to commit to that pet. Too often people buy reptiles as kids and then get bored of them and re-home them. If you want to convince her you are ready, show her your answers to those questions I've asked, show that you realize how long of a time that is and your plan to take care of the gecko and deal with any challenges that arise over time.
I might have to agree though with your mom here, I would recommend waiting until you are at least 16-18 years old before you commit to a pet like that. (again, not sure on your age).