You'll do yourself a favor to not insult people over technical details. The arrogant attitude does not give a good impression. If you wanted to make it known you knew something they didn't, you could have achieved much more with "Belize and Central-America for that matter is considered to be part of North America, and very explicitly not part of South America". There was no need to make a point of someone knowing less, or disparaging their argument that had little to do with this.
In any case, do not mistake my interaction here as some sort of personal investment. I do not care much. Take the advice from a stranger as you will.
My desire: People with strong opinions should temper them. Or at least temper them in public. That's all.
Total fucking non sequitur!
(Even trying it on paints you in an ever worse light. At least in my book, you'd have come out of this a lot better if you'd taken GP's advice and backed off gracefully one or two comments earlier.)
I've spent a fair bit of time in Central America, and the people I met there generally took great umbrage at being referred to as "South America".