They are just being protective. I'm sure you know that german shepherd dogs are like that. They are very aggressive guard dogs that will protect till the end. My own GSD has bitten several people that have stuck their hands through the fence or into the car. (though she would never bite a child), and she barks like nuts when people go by. It's a nature that I wouldn't want to get rid of. You never know when you might need it!

I don't think obedience classes would make them want to protect you or your home any less, but it's a good idea anyways, you should try it.