First and foremost, I want to applaud you for your ambition. Very few people do this kind of thing...and let me point out a couple reasons that might be issues with your parents.
1) Are you under 18, or over 18? Remember, as a minor, you have much less ability to deal with certain situations alone. For example, there is a lot of liability. Your parents may just be concerned that you won't be able to handle yourself in a dangerous situation. Most projects go by without a glitch, but there is always that issue.
2) Have you travelled alone? Really, alone? I don't mean on a school trip for robotics, or to the next town over, I mean international travel. I thought I knew everything about being on my own when I went to Spain to study abroad this summer without Mom and Dad to take care of the technical stuff for me - boy, was I wrong!!! I had a VERY rewarding experience, but I also came to understand how much difference there is between travelling on your own and studying or volunteering, and being a tourist.
3) Are you already responsible? I don't want to pass judgment on your character - I'm sure you're great if you're even considering this - but you may need to really prove yourself first.
So let me present a couple solutions, and expand upon what other people have mentioned:
Step 1: You need to prove you can be by yourself and handle a service project.
Find anything where you can volunteer. Do some work. Be on a schedule. Show your parents that you won't just slack when you actually have to work. Work outside. Work hard. I don't know your skillsets, but you do - take advantage of them.
Step 2: Choose a volunteer opportunity that will apply to an international project
Sure, cleaning pet cages at the Humane Society is a great volunteer effort. But will it really help you nurse natural disaster victims back to health? Will it help you construct a house for a family in need? Will it help you build a well, or repair a school? Not entirely. Choose volunteer opportunities that will apply to not only your volunteering goal, but also to your future. A few examples...
Let me call out some examples:
Imad mentioned he volunteered a LOT at Smithsonian. He's also going into engineering. Smithsonian is sciency - a good resource for connections, a good opportunity.
I am going into Medicine as a career. I have volunteered for two years as a breast cancer researcher and lab techie at a Breast Cancer lab in Purdue. What I'm learning now applies a LOT to what I'll be doing in the future.
You don't necessarily need to connect your volunteer opportunities, but having those connections is great because you have a natural follow-through of activities. As soon as you prove to your parents you can take a step, then they'll be much more likely to let you take a leap. Good luck
