The last time I cycled on the pavement was over a decade ago, when I was a toddler on a push bike. I can definitely see why some people would prefer to cycle on the pavement; 5 cyclists have been killed on London's roads in the past 9 days. A very frightening statistic. You have to bare in mind that it is illegal to cycle on the pavement for a good reason though. People can and do die from getting hit on the pavement. The only reason why the number getting hit isn't high is because the vast majority of cyclists cycle on the road. Imagine popping round to your neighbours, crossing the fence, and a cyclist traveling downhill hits you.
You can relate cycling on the pavement to cycling on the road in a way that
--The cyclist on a large metal bike, to the toddler popping out from nowhere is the same as the truck driver in a HGV, to the cyclist that turns a corner though a red light.
In this instance, you are the larger object carrying more momentum. The fact that your chances of being injured are less does not justify cycling on the pavement as you pose a real danger to members of the public (and yourself if you cycle into a reversing car)
You could probably get away with cycling slowly at a quiet time of day in the suburbs, but cycling on the road can be safe if you take appropriate measures. For example, wearing a high-vis jacket and a helmet. My local council ran a cycling scheme where every resident was given the opportunity to attend 1 on 1 cycling lessons with a qualified instructor. I had two sessions and learnt invaluable skills about road cycling. I now cycle regularly, averaging 10 hours a week (which includes a long 4 hour club run) The more cycle, the faster you become and I now find myself overtaking 2 or 3 busses on a particular bus route. I really recommend becoming aware and confident with cycling on the road as the convenience and health benefits are huge. Hope everything works out!