Times have changed. I was a little slow to get rid of training wheels at age 7, but once I did, I was allowed to ride up and down the street. About a year later, I was allowed to ride "around the block," a distance that was open to some interpretation. It wasn't long from that point that I was given free reign of the neighborhood. My parents and grandparents bought me my first LBS bike at age 15, and the following summer I got my first job at a nearby neighborhood hardware store. Might have been 4 miles from home at most. I had to cross a semi-major road to get there, but that was just a matter of being careful. I came up with the idea to ride to the store, and my parents were proud of me for thinking of it. By the time I turned 18, they would have let me ride just about anywhere I wanted to, but by that time I rarely took advantage. Cars were more cool even though I still rode the bike.

There's nothing wrong at your age with trying to have a reasoned discussion with your parents about this matter. But becoming defensive and confrontational isn't going to help. I'm not quite old enough to be your dad, but your route sounds no more dangerous than what I rode at your age.