Why do some people say there is not a Central America?
Because they flunked grade school?
Geologically, Central America is part of the continent of North America. Same with the Caribbean.
There is central America and I don't want the USA to be central or south America
Which people say that? It's not a reliable thing to consider views of random people. Many people you speak to will give an opinion when knowing very little on the topic they are speaking of. Much better to use a proper informed geographical source to find the information you need. That will be reliable.
In the same way there’s no “Rust Belt” or “Bread Basket” in the atlas, but they’re still widely known nicknames for the regions. Maybe those people memorized an atlas.
Technically speaking, in terms of continents, there is only North and South. North AMerica and South America are continents. Central is not.
And these people are?