Well although you've ridden a cruiser bike, it is somewhat similar because it is a bike in general but, more so you are riding a bike that is meant for cruises and not really meant for tearing up the street that a street sport bike usually entails. Because your dad rides means that you have a good chance of owning your own bike as well, because it would be hypocritical if he weren't to let you ride. The reason why your parents won't let you ride a sport bike is because of the stigma it carries.
Maybe your parents dont want you to ride a Sport bike because they think it will kill you faster then a cruiser. It really doesnt matter what bike your on, cause either way you are invisible to all the cagers anyhow. But what matters to your parents is that a sport bike has the abilities to do more on the street then a cruiser will. PLus with the temptation of stunting might give your ego a boost and cause you to fall and have an accident.
If you are intent with a sport bike, get a Ninja 250/500 and prove to them that although the ninja 250/500 is under the 600 sport range it will atleast give them a sense of peace that you are willing to start at a lower cc bike and to prove that a sport bike can be just as safe as a cruiser. Then when they've felt comofrtable with you riding on your own then maybe they will let you buy your R6.
Whatever you do, DO NOT go and buy an R6 and try to hide it from your family, one way or another they will find out and they probably wont let you ride ever again. ANd when you get into an accident it is something that your parent s wont be to happy to hear.
Good luck though