I've even debated on this topic within these forums from the Minarchist position!
What did it for me? I started listening to Stefan Molyneux and I had seen a few Larken Rose videos. At first I'd only watch one of their videos when it was linked and relevant to a certain forum topic around here. Eventually, I started digging through their Youtube channels at which point it was only a matter of time.
I think one of the big points that convinced me to switch, thanks to Stefan, is that small governments end up as the most destructive governments because they can leverage the free markets and all it's technological advancements. Also, his points on why foreign invasions are unlikely were quite persuasive.