matthewzguitarz,
As unlikely as this will seem, your parents really are on your side. In fact, they are probably the most on-your-side people you will ever meet -- even when they don't know how to talk to you. (I'm assuming, from the tone of your post, that you have not been abused as a child. There are exceptions, of course.)
If they say that they have concerns, that's an open door for you to try and talk with them. The fact that they sat you down shows that they're trying to figure out what to do -- which is to say, HOW TO HELP YOU. It's going to be hard to find the right words, I know, but you need to tell them what you're feeling. Don't wait for them to bring it up again. Find a time and start talking. If it's easier, talk to them individually. (Years ago, I told my mom I was trans, and she told my dad. That made it a whole lot easier.)
Odds are that they already know, at least sort of, what you're wrestling with. The best thing you can do is practice what you might say while you are alone. If all you have is questions about yourself (as we all start off with), that's fine. Tell them that. You don't have to go into any great detail, or even spill everything, just get a conversation started. Then answer their questions.
If you tell them, if you even TRY to talk to them, they will in turn try to help you. If you don't, you're potentially cutting off the best source of support you'll ever have (for all things, not just transition or whatever).
I know that this sounds impossible, but having the hard conversation is always better than avoiding it. What's the worst that could happen? (Exception: History of physical or emotional abuse.)
Lora