When you talk to and anti, being combative and aggressive is not the way to go. Be polite and calm even if they aren't. If they start getting agitated, don't respond in kind.
It is helpful to say that you understand their concerns... We all agree with that mass shooters are awful and are frightening, and that establishes common ground.
You can counter by pointing out that a home invasion is also frightening, and that the cops do not have the ability to respond in time.
If you are polite and reasoned, you have a fighting chance of winning someone, and a very good chance of planting our counter-position that gives them pause.
What you have the best shot at is showing an anti that a gun owner can be a nice person. That matters a lot.