I am a gun owner, but I believe private businesses should be able to ban the carrying of guns, open and concealed, on their premises. It would be great if we could ban the need for handguns, but until we manage to eliminate crime, that isn't a possibility. I know of several businesses that ban the carrying of guns on their property; I simply take my business elsewhere. Two of these places have been robbed during daylight hours by armed criminals... I guess advertising that you don't allow guns on the premises didn't bother them in the slightest.
A business is private property and business owners are allowed to refuse service to anyone they please as long as they aren't being discriminatory. Gun owners are not an endangered class. They are not protected by anti-discrimination laws. Therefore, business owners should absolutely be allowed to ban open carry of guns if they so choose.
Guns should be banned, period. However, in relation to the argument that private businesses should be allowed to ban open carrying - businesses are responsible to their employees in the workplace and should be able to deem certain things appropriate or inappropriate. For workplace safety, the banning of guns should not even be a question.
You have the right to ban guns from your home. When you open a business you are no longer private. A business can't ignore any of my other constitutional rights, so why should they be allowed to ignore the 2nd amendment? SCOTUS has ruled that private businesses can't discriminate based on rights that aren't even in the constitution, therefore they certainly can't discriminate on a clearly defined one.