To the OP: suggestions for helping your parents understand your POV
First of all, the best thing is that neither you nor your parents think the other is nuts. This also means that your most important job is to keep it that way.
Rather than lecture them about the matter at hand, or even just expressing your thoughts, you may want to ask questions, questions that require thought and consideration. When your folks come back with a typical anti knee-jerk response, refrain from immediately pointing out the obvious-to-you logical fallacies. Let a few days or weeks go by to let them think about it, then ask the question again, perhaps in a different way, and/or ask for clarification, e.g. "I understand what you are saying, but this part of your answer doesn't make sense to me...can you explain?" Or, if their perspective is based on unspecified concerns, "how can I convince you that I can handle...?" Sooner or later either their logical house of cards will come tumbling down, or you will reach an impasse at a core belief you do not share. Either way both "sides" will be a lot closer to understanding the other. With understanding comes acceptance of, and sometimes, respect for another's perspective.
It is easier and more effective to lead someone's way than to push them in a direction they're reluctant to go.
I think ProShooter's class-with-a-parent suggestion is great. "I've already told you I intend to buy a handgun when I am of age, don't you want me to know how to use it safely?" Hopefully, you will get a "yes" to that. "How will you know whether I am handling it safely if you don't take the class too?"
Be patient, you have the advantage of plenty of time to let your situation mature to where you want it to be.