Is Mexico part of North America or Central America?

[True Federalist (진정한 연방 주의자)]

Geologically there are six major continents: Africa, Antarctica, Australia, Eurasia, North America, and South America. Central America isn't geologically part of either continent, being part of the margins of the Caribbean and Panama Plates. Geologically, Mexico is North American.

[True Federalist (진정한 연방 주의자)]

That would be easily solved if the term America was abolished. Or just let US have it for themselves if they really want it and change the name of the two continents instead to two different independent terms.  People can come up with something respectful to the Indigenous tribes who are the true owners of this land while also ending any link between North America and South America as if they were subdivisions of one continent.

Highly doubtful. The Americas were extremely diverse linguistically pre-contact, with tens of language families and lots of language isolates with no known relatives. It would be impossible to come up with any term that would be respectful to more than a small subset of them, even if we limited ourselves to such languages as are still in use.