To add some more clarity, Central America is a region within the continent of North America.
ETA: Perhaps the OP’s question should have been “Why isn’t Mexico considered part of Central America?”
Apparently, Lonely Planet doesn’t believe so, either. I know, it’s an unusual definition of “Central America,” but lopping Mexico into Central America isn’t exactly unique. A better term would be Middle America. In any case, both are subregions of what is generally considered North America.
I love it when people start talking in technical terms! So much more precise your answer is. 
A fuckload skinnier is Central America. 
Is this one of those entertainment threads? Thanks OP!
Of course those who say Mexico is part of North America are “going by convention.” Because “going by convention” is another way of saying that Mexico is part of North America because that’s how the continent is defined. Wikipedia says, “The continent is delimited on the southeast by most geographers at the Darién watershed along the Colombia-Panama border, placing all of Panama within North America. Alternatively, a less common view would end North America at the man-made Panama Canal.”
If you want to define North America as including only the USA and Canada or whatever grouping you wish to make, you’re free to do so. However, the rest of the world may not agree with you.
Hey man, whatever you believe.
And don’t be surprised if the smart people make fun of you when you do so. That’s how those smarty pants SMART ASSES are. 
North American was defined back in 1986 when Canada and Mexico arranged to engage in a trade block designed to integrate centralized planning into the market based USA. Hobbled by commitments to the emerging New World Order George Bush I tacitly agreed to NAFTA and the proposed super highway designed to not only facilitate troop and goods movement north and south but to break the American Midwest into 2 smaller east/west populations all the better to allow eastern/western elites to exert control over the state legislatures through the interstate commerce clause.
How does no one not know this? :dubious:
If the OP looks at the tectonic plate map here File:Plates tect2 en.svg - Wikipedia they’ll notice that Canada, the US and Mexico are all on the North American plate. Though I’ll note the OP also forgot about Cuba, Jamaica et al. normally being included in NA.
He probably doesn’t believe those latter places exist.
So Europe is limited to those countries that are part of the European Union, i.e., Switzerland is not in Europe?
Of course not, that would be stupid
Europe was defined back in 1951 by France and Germany (using Italy’s inclusion to ensure Luxembourg wouldn’t bolt) to ensure further expansion of labour based pan-nationalism, when designing the ECSC.
Do they teach you nothing in Australia? 
But geographically-speaking Finland is part of continental Europe. There’s no debate about that, as far as I know. With México I don’t think it’s as clear-cut. I think it’s very easy to say that México is part of Central, not North, America even geographically.
Neither is North America!! From a land mass standpoint it’s really all just “America” from the northern-most tip of Canada to Cabo de Hornos (“hornos” translates as “ovens,” by the way - not “horns”). Heck, I remember that back in high school one of my instructors told us that many thought of Europe and Asia not as separate continents but as one large one - Eurasia. But politically and culturally Laos is clearly quite removed from, say, Norway. That’s why many make the distinction between the two (meaning: Europe and Asia, not Norway and Laos), I’m guessing.
“Clearly,” eh? Okay - which continent is Turkey “clearly” part of: Asia or Europe?
Ok, do you understand that Central America is not a continent? Now you might suggest that it should be, which would be a bit different from the way you asked the question. If you look at the Wikipedia cite I provided you’ll see that there is a dividing line in Mexico where the Pacific and the Caribbean Sea are closest to each other, and that would be a natural location for the northern extent of Central America, placing Mexico partly within it. However the border between Mexico and the US is rather arbitrary, so using that geopolitical border as purely geographic one doesn’t make much sense to me.
To paraphrase from Stripes, our ancestors got kicked out of the best countries on earth. Look…his nose is cold!
So you’re saying that “North America,” technically speaking, extends from the northern-most point of Canada down to Panama? Well if THAT’s the definition then yeah - I guess México IS part of North America, then. But linguistically and culturally I still don’t think that makes much sense. For me the U.S. and Canada are “North” America. Every other country on this continent simply isn’t.
Really? You do know the Anatolian peninsula part of modern Turkey has been considered part of Asia since antiquity right? Heck people even call it Asia minor.
As others noted up thread, what’s your thoughts on French speaking Canada then? Linguistically and culturally they aren’t any more different to the US and Canada than Mexico is. What about the Cajun south? Are they part of North America? What about the South West?
This Canadian says your wrong. Since I’ve got a bigger country my vote counts for more. Mexico is in. I’ll even allow Bermuda and those flighty French islands in the Gulf of St. Lawrence.