The typical version that gets used on gun control advocates is to call anyone who supports gun control and is still willing to rely on support from armed guards or police for their security a hypocrite. After all, shouldn't they be more worried about the potential consequences of having more guns around than they are about the increased risk that would come from not having the security?
Of course, I'd argue that most gun control advocates have less of a problem than one would expect with a limited number of guns being in the hands of people who are very well trained. This is generally the purpose of the restrictions they argue for, after all. Only a gun control advocate who believed guns have no benefits at all could be a hypocrite in this way - and most of the ones who believe that strongly won't be using armed guards anyway.
Then the version that gets used on gun rights advocates is that many of them perfectly willing to create gun-free zones if it benefits their security, as in stories like the one from this blog post. Shouldn't they feel that allowing everyone around them to carry guns would only make them and everyone else around them safer?
I've never heard a gun rights advocate defend that idea, but I'm sure one probably could try to argue that there are situations where the objective is the security of a specific person that demand more caution than should be the norm. I'm curious if anyone has a better idea, though.