That link centers the map on Prince Ave in Athens-Clarke County. Look that road up, it's a 4 lane road. I would never bike on that road, of course it's dangerous. If you avoid roads like that, you avoid most of the risk. It's common sense but a substantial portion of adult male cyclists obstinately refuse to apply such common sense because they'd rather die as some sort of martyr for their right of way than stay alive.

In fact most of the roads on the map you just linked to are marked as green. If I zoomed out and the first red road I saw was Broad Street. That is four lane road as well. No surprise. Multi-lane roads are very dangerous for cyclists and pedestrians, so you should tell your children to avoid them. That's what I've always done, so I have much less to worry about than the crudest population-level statistics would suggest.