All my friends are out spending time with each other?

I am 16 years old and yes, still living under my parents roof but there is no shame for me in saying that. I'm very close with my family and even all my cousins and I feel like we're siblings. Since I was brought up in a traditional family, my parents are also quite conservative but I don't drink alcohol, smoke or have sex, nor do I try and sneak this behind their backs. It's just lately, as it's summer, all my friends and classmates are out together. I don't belong in a big gang but I have a few close friends who I wanna spend some time with also, because I feel like if I don't we'll drift apart.. but my parents hate it when I try to find an excuse to get out of the house because they say that they're doing this for me in the long run and I'll thank them for it, then you get the 'kids go missing every day and they don't know what they'd do if that was me' etc. which I understand but how do I feel like I still have some sort of social life. Were your parents protective over you and did it benefit you in any way?