Duno about #18indycolts, but for most police and military represent agents of the State. Police have been endowed (domestically) with the authority to act within the laws to apprehend and submit to the courts any person they feel to be violating the law - using any amount of force up to and including deadly force to effect that apprehension. Police act with the entire authority of the State, and as agents of the State they represent far more than "just a woman or man with a gun".
And with respect to Dust Monkey's question:
Originally Posted by Dust Monkey
"Then why do liberals scream that only police and military should have guns?"
...the answer is similar. Liberals believe that the responsibility for the protection of society and it's citizens belongs to the State, not to the citizens themselves (whom they occasionally accuse of 'vigilante-ism'.) They perceive firearms in the hands of citizens to ultimately create more crime and accompanying risk than more 'freedom'. From a liberal perspective, society must give up some 'freedom' to be more secure from risks that result from firearms.
While it may be true that in the absence of firearms, there would be a substantial reduction in firearms-related crime (or accidental death), complete social disarmament remains a utopian ideal. England and Australia provide eloquent examples of what happens when State authority is used to disarm the citizens. Risk is by no means reduced, for reasons that go well beyond this thread.