Personal opinion:
Antis are divided into four groups:
1) Those that want control. This includes most fascists and socialists. These people realize that imposing their social agenda on the public requires that the public be mostly disarmed; otherwise there will be bloody and effective resistance. Many in this group tend to become leaders in the gun control movement, though gun control per se is not their driving force.
These people cannot be swayed from gun control unless you can change their socialist / fascist leanings as well.
2) Those that envy people who have guns. Not for their wealth, or even for their power, but for their self control. These are the antis who honestly believe that mere possession of a gun will cause people to become violent .... because that is what they would do. These are the people you hear about in the news, who get into fistfights at their kids sports games over a call the referee made or who run someone off the road and start a fight with them because they were flipped off in traffic. They have little self-control themselves, and what they have comes from fear of starting something they can't finish. They tend to be prone to substance abuse and addictions. They have an inborn desire to control others, because they cannot face a world where they would have to control themselves (as opposed to being controlled by laws and the threat of force).
These people need serious counseling before they can be swayed.
3) Those who view firearms as useful for hunting, law enforcement, the military and even self-defense, but who fear what others will do with them. These people have bought the "needs based" argument hook, line and sinker. They are usually afraid of some specific group of people (whites, blacks, minorities in general .....) and are willing to support gun control laws as long as they perceive those laws restricting that group more than they are. They are the fifth column among us, and are perhaps our most dangerous enemy .... because they masquerade as our friends. They are the ones hard-core antis aim at converting, with sound bites about how "no one needs an AK to hunt deer".
4) Those that fear firearms due to a lack of information or due to misinformation. They believe the lies regarding guns because that is what they have been taught. They often have little first hand knowledge of guns, and what they have was often gained in a manner that emphasized how dangerous / destructive guns were, and did not point out many uses for them other than hunting or the military. In their lives, they either have little need for guns, or they are so brainwashed that they cannot see the use for one even when they have the need.
These are the vast majority of fence sitters and antis. Thankfully, most are susceptible to reason. Most have so little exposure to firearms; they have almost no factual basis for their beliefs. Yet at their heart, most are thinking people. If you can gently correct their misperception on one single element of the gun debate, they will gradually come to question other parts of it.