During the "Conversation", you will be asked...

"Why do you carry arms" or "why do you WANT to carry arms"

Instead of blowing off the questioner with a simple answer such as "because the Seond Amendment says I can", which, while true enough, still lacks that "savoir-faire" that will convince a liberal, try some or all of these:

• "Because there's danger out there, and not enough cops, so YOU need some protection and I'm willing to create it for you. Aren't I a nice guy?" This could be called the "sheepdog" gambit, but as with all chess gambits, it might not work, so be prepared for that.
• "Because the level of danger we all face from criminal activity every day varies, and is also unpredictable, and isn't going to be changed with any gun bans (see England, Australia, etc). I don't know about YOU, but I have better things to do on a constant basis than continually having to evaluate my danger level and react by avoidance, like YOU have to do." This is called the "Risk Management" solution. You should be able to sell this if you keep the snark level down.
• "Because I've grown up carrying guns, have gotten used to doing that properly so that it won't impact YOU at all, and it is the simplest way for me to handle the variety of dangers I face every day. Bearing arms give me options for handling danger that I can't get in any other way except by hiring professional bodyguards, and I'm not rich enough to do that." This one could be called the "trained and ready" explanation, and it might have the best chance, depending on how skeptical of the first two the liberal person might be.

All three of these explanations may be appropriate for you to inform your liberal friends/relatives with. If so, do so.