Like it has been said, changing someone's mind is not easy if they are already dedicated in their mind to their beliefs. It is just like trying to convert someone to a different religion.
However, you best defense is having well thought out answers to questions/accusations they might have. You should be a voice of reason, and not spout off random facts and quotes in an aggressive manner.
Calmly and articulately explain your personal reasons for owning a firearm. They will ask you questions that they think you will not have an answer for. Prove them wrong by giving well thought out answers that they would have a hard time arguing against. If you go on the offensive, all it will divulge into is a shouting match or statistics.
On thing both sides of the argument love to bring up are statistics. The fact is, statistics are mostly bullshit. There are plenty of stats on both sides of the argument people will throw around. You should know them all, but at the same time you should point out that no statistic is going to be accurate in a real life scenario. There are too many variables with correlation vs causation. All statistics show is a snap shot of a small group with no way of factoring in all of the different controls.
I tend to shy away from bringing up the politics behind it, because political views are the hardest to change. Instead, I focus on physical, tangible and practical data points on a personal level. Show the reasoning an individual might have for supporting your beliefs.
I'll give an example, it's kind of a long answer, as I tend to verbose too much.
If the accusatory question is "Why do you need an assault rifle to defend yourself with!?". This is the answer I usually give.
American civilians have owned semi-automatic, magazine fed rifles since 1909, when they were first introduced. Materials, and looks may have changed, but it is still the same essential function. A rifle that fires once every trigger pull and has a detachable box magazine. This is not new technology. There many advantages that a rifle like that offers over both handguns and shots. They are easier to aim and accurately fire than a handgun, while also being much more powerful. They are easier to use, and only have about a 1/4th of the recoil of a shotgun. They are easily adjustable, and usable by anyone regardless of size and strength. There are also many studies done that show a high velocity rifle cartridge will penetrate less number of walls when compared to either a handgun or shotgun round. They also offer a larger capacity magazine, because I do not get to choose how many shots I may need, if I ever needed to use it. I do not get to choose when, where, and who I may have to defend myself from. The aggressors always have the advantage because they were ready, and I was not. The only variable I do have control over is having the most capable tool possible at hand.
See, something like that not only brings it to a personal level, but also raises points of practicality. Just spouting off "because I can!" doesn't back up your points at all.