My family thinks i have an eating disorder?

alright so this is rlly beggining to get on my last nerveee. i have a big family-a whole bunch of siblings and all except one, my bro, are meat eaters but he is vegan like me. i recently switched from vegetarion to vegan and i love this new lifestyle. i feel so much heathier. but my family is CONVINCED that i never ever eat and im trying to loose alot of wieght. im not. i just keep my body in shape. i am skinny, and they are afraid im loosing to much wieght, when rlly my body is just getting more otned cuz i run about 3-4 miles a day and take tennis lessions 3-4 times a week, so im very active. i loveee green tea, hot tea. i drink it all the time as well as water. they think i drink it to speed my metabilism buti drink it cuz i love tea, always have. i do eat tho, i just eat lightly and healthy cuz im vegan so i dont eat cookies,icecream,cake,pizza,fries, or anything else thats unhealthy. so im just skinny cuz i love to be active and healthy. they are so convinced tho that 2day they like had a freakin intervention and when i defended myself they said anerexics get defensive, i was like wat else am i supposed to say!? my sister wuz like "we know wat ur trying to do, ur trying to loose wieght, its obvious" and my mom said shes upset with me for going vegan. its not thier life tho, ik they are my family, but its not thier bussiness wat i put in my mouth and wat i dont.im goign to stand up for wat i believe in, i hate meat and dairy and i NEVER wanna associate with it. i dont know how to handle this, they see me eat-but since its not fattening meat and stuff they assume im not eating protien and calcium.how do i show them i odnt have an eating disorder!!??