There are no responsible gun owners, only lucky ones.
Keeping a gun in your house is like keeping high explosives in your garage. It doesn't matter how careful you are, all it takes is one unlucky slip-up to bring tragedy to your family or your neighbors. No matter how many precautions you take, you're still creating a dangerous situation for the entire community by your actions. Keeping guns in your house is an inherently irresponsible thing to do.
All tools of destruction have their uses. We don't ban high explosives entirely; we treat them with the respect they deserve. We keep them locked up away from where people live in order to minimize the harm if there's an accident. We keep a careful accounting of who has access to them. And we don't give people access unless they can clearly demonstrate why they need to have it.
We need to treat guns with the same degree of respect. If you want to own a gun, you should have to state why you need one, and then regularly demonstrate that your usage conforms to that need. If you're a sportsman, you should be required to store your weapon at an approved club with clear procedures for signing it in and out. If you want to contribute to community defense, you should be required to store your weapon at a neighborhood armory with similar safeguards in place. Before anyone picks up a gun, there should be a volunteer who looks that person in then eye and asks himself "Is this person who they say they are? Are they capable of making life or death decisions? Are they calm? Sober? Sane?" And if the answer to any of these questions is "no", the gun cabinet should stay locked.