As I mentioned earlier today JPFO has a booklet--Do Gun Prohibitionists Have a Mental Problem?  Here are some of the mental problems mentioned in the booklet:

1. Projection--A person cannot accept their own feelings because they are bad, wrong, or forbidden so they project them onto others.  A typical anti-gun person that uses this mechanism might have feelings of unconscious rage toward gun owners, project them onto the gun owners, then have a conscious fear of gun owners.
2. Denial--A person refuses to accept reality because that reality is too emotionally painful.  A typical anti-gun person that uses this mechanism might believe that the police are all anyone really needs to protect them from attack by criminals or that a tyrannical government could never happen here.
3. Reaction formation--A person turns an unacceptable feeling or desire into its complete opposite.  A typical anti-gun person that uses this mechanism might have a murderous rage toward his fellow humans and then claim to be a pacifist and believe they are “superior” to “less civilized” people who engage in “violent behavior” such as hunting or target shooting.

The booklet goes on say that pointing out the mental problems to the anti-gun person isn't going to be very productive.  What you need to do is:

1. Make the person feel safe, then provide experiences and information to help him understand the positive aspects of gun ownership.
2. Be gentle.  Defense mechanism protect people from feelings they cannot handle.  If you take that protection away, you can cause serious psychological harm.  And because defense mechanisms operate unconsciously, it won't do any good to point out to the anti-gun person that he or she is using a defense mechanism.
3. Use the mirror technique.  Feed back what the anti-gun person is telling you, in a neutral inquisitive way.  If someone says that people shouldn't own guns because they don't want to be killed if their neighbor had a bad day, you might respond, “So you fear if your neighbors had guns, they would use them to murder you.  What makes you think that?“  It's important to ask “open-ended“ questions that require an answer other than “yes“ or “no“.  Such questions require he anti-gun person to actually think about what he is saying.
4. Don't try to “win“ the argument.  If you are arrogant, hurtful or rude to the anti-gun person, you will only convince him that gun owners are arrogant, hurtful and rude people--who shouldn't be trusted with guns.
5. Respond sympathetically to the plight of the anti-gun person.  If they believe they are surrounded by people that want to kill them and their family if only those people had a gun and they could do nothing but wait for the inevitable they lead a terrified life.  Invoke your own compassion for their situation.
6. Provide corrective experiences.  Corrective experiences are experiences that allow a person to learn that his ideas about gun owners and guns are incorrect in a safe and non-threatening way.

There is a lot more material in booklet.  Many of the JPFO “Gran'pa Jack” booklets are for giving to anti-gun people.  This one has probably is better utilized by distributing it to pro-gun people.  Although I haven't done that with this one I have purchased a few hundred of their booklets and let the local sporting goods store give them away.  I've also given them away at Boomershoot events and local IPSC matches.

Update: See also the more complete version here: Raging Against Self Defense.