I went vegetarian at the age of 14 and got a lot of criticism and questioning from my family. The reasons were three-fold:
1. Concern for my health
My parents had very genuine concern for my health, so I always complied with their request for more information on my diet. I saw a nutritionist, talked with my doctor (with my mom in the room), etc. I studied about B12, protein, and other nutrients, so that I was prepared to field my mom's questions about how I would get enough of this, how I would substitute that, etc.
If you are a minor and living under your parents' roof, I'd argue it's within their right (and in your best interest!) for them to question seriously your new diet and to have continued discussions about your health. By engaging with them in these discussions whenever they wanted I learned they became much more trusting of my making my own eating decisions and much more comfortable with my choice.
2. Inconvenience
For legitimate reasons, my family would complain about my vegetarianism. For my parents, they were concerned about the additional burden it would place on them to prepare well-rounded meat-free meals. I did what you did- I ate everything except the meat portion of dinners, or I'd bring out yogurt, cook up an egg, etc so they saw that I wasn't just 'going without' during dinner.
Offer to make dinner sometimes- veg lasagna, eggplant parmeasan, and veg chili are big family hits. Your parents will be grateful for your willingness to help them cope with your diet and everyone will be happy to enjoy new tasty foods. (Plus everyone will realize veg food doesn't have to just be a plate of celery- it actually tastes good!)
3. Annoyance
For my siblings, and to some extent my mom, it was annoyance at this 'fad' was just a ploy to get attention and express myself. Whatever you do, DON'T preach your opinions about vegetarianism. Don't try to change your family members' opinions about eating meat. Respect their choices and they will start to come around and respect yours. Don't make a big deal about ordering at restaurants or draw attention to your vegetarianism at meals- it is only annoying.
If you help make yummy meals and you are always wiling to talk to you parents about nutrition when they raise concerns, they will understand vegetarianism a lot more and be more comfortable with it. A lot of their concern is out of just not knowing much about it, so the more they learn the less they will rail you about it.
That said, if you have younger (read: annoying!) siblings, they will always rail on you

My little brother tried to convince me for years that chocolate has meat in it so I couldn't have any and he got to have my piece, haha. Just let is brush off.
The less attention you draw to your eating styles, the less your family will notice or worry about it.
For me it definitely took a good year to get there. After that they didn't really think twice about it.