Living in Kalifornia I've had my share of interesting conversations with people who have never used a gun in their lives. Many of these people are simply ignorant or misinformed. Others have some kind of background that keeps them in a state of denial about the usefulness of firearms.
I've broken this down into a few broad groups, as I see them. Once you can identify why someone is anti-gun or gun-hostile it's often easier to deal with them.
Religious belief
This is the person who will tell you the Bible says "thou shall not kill" and thus guns, as an instrument of killing, would go against God's word. Never mind that the original Hebrew was "Thou shall not murder" -- there is a huge difference between murder and killing, say, a rapist. Other examples exist in the Bible to counter this thinking as well (others will be more versed than I).
The Victim
Pity the poor victim. Listen to their traumatizing tale. Perhaps that's harsh, but many anti-gun types have shaped a whole opinion based on a single incident. A relative committing suicide. Being robbed at gun point. An accidental/negligent discharge. Whatever the scenario, their whole belief system is based on the idea that if the gun was missing from the equation the resultant incident would not have happened or would have been lessened somehow. So now all guns are responsible for the incident. I usually point out that their reaction is understandable, but wrong. I compare their desire to remove guns to the MADD campaign. Rather than blame cars and trying to ban them, they focused on the illegal actions of people and educated us on the dangers of drunk driving. A similar campaign would seek to educate people on safe gun handling, marksmanship training or identifying people in emotional crisis instead of trying to ban a useful tool. Unfortunately the emotional aspects frequently overrule their logic and they cannot or will not deal with the fallacy of their position.
Note: The same claims could be made for people with CCW's who carry after being victimized by criminals. However, the difference is that obtaining a CCW is a personal choice that is not forced on others. Where "the victim" blames the object, rational people see the criminal as responsible for the incident, not the gun.
The Philosophically Enlightened
These are the people who will tell you there's always an alternative to violence and that violence begets more violence. They'll describe how non-resistance "takes away the agressor's power" and that resorting to violence "lowers" you to the level of the common criminal. Obviously these folks have never been beaten and robbed, threatened with a knife, held hostage or faced a person seething with enough anger to wantonly kill a roomful of Nuns. But ask them what they'll do when they enter their child's room at 4 AM to find an intruder holding a butcher's knife over their head in one hand and their child by the throat with the other. There is no time to debate or argue, no time to call 911. I asked one person this and their answer was disgusting to me as they could not conceive of using violence to save even their own child. The good news is that these people CAN be enlightened a little at a time, unlike the loonie liberal left.
Loonie Liberal Leftists
Dyed-in-the-wool loonies don't need logic, reason or facts to have an opinion. Just sound bytes and headlines. They parrot the well-known slurs against guns & gun owners (Gun owners are murderers who haven't killed yet!). These are easy to spot as their lack of thinking will often clearly show up when you reverse a situation on them. They'll ask you why you hunt when you can buy food at the store. But ask them why Eskimos are still allowed to kill whales and "it's part of their heritage" -- but they'll deny hunting is an American heritage. They'll spew the rhetoric that without guns society will be safer, to which I point out it'll be safer for gangs of toughs preying on the small, the weak and the elderly. They'll point out that the power of modern guns were never envisioned in 1787 so we're limited to muskets. In that case the 4th amendment doesn't prohibit wiretapping, computer privacy, electronic records of any kind, etc.
Living in Denial
Here is the soccer mom, the medical professional, the college professor or other person who's life is centered in a good community. About the most violent situation they deal with is a fist-fight between young boys. They see no need for a firearm in their home since they don't even know anyone who's been the victim of a serious crime. And if they don't need a gun, certainly you don't either. Crime only happens to those "other people" on TV or in the papers and they think it's likely because the victims were in a bad area or were involved with shady characters. They live life denying that crime can happen to them, their families or someone they know.