Honestly, the "Latino/Hispanic" label is confusing now. I used to think as a kid that it included people from Spanish-speaking countries. When I learned it can include people from Romance-language speaking countries, I wondered if Haitians like myself could be considered Afro-Latinos like some Dominicans and Cubans
I think of it as a label for those who are perceived as coming from the south of the US. To some Americans, all Latinos are Mexicans or some variant. But it seems to be used to make a distinction and preserve culture. Like what many mentioned before, many Irish, Italians, and other Americans of straight European descent consider themselves "white" or "American". They have assimilated easily since they can speak English and barely have connections with their country of origin. They also enjoy being a part of the greater American culture.
The group of people known as Hispanics are mixed. Mexicans and Brazilians of only European descent who are first or second generation Americans may or may not consider themselves white depending on the circumstances. I once knew a blonde blue eyed Cuban girl who didn't consider herself white. Part of the reason is culture. Standard US culture is different from the ones south of us. Hispanics who are meszito or mixed with Native American/European more often than not don't identify with being "white". This is probably caused by their own choice like the full or mostly European crew or by existing Americans categorizing them as too "brown" to be in the white club (For lack of a better term).
There are also the Latinos who are mostly of Native American or African descent and they will most identify as "Latino" since they can't identify with white culture. Some (who are African-descended) may identify with black culture, but the ones who are your average Mexican or Peruvian of mostly Native blood will settle for being Hispanic for as long as they are seen as "brown".
I don't mind if the "Hispanic/Latino" label persists. As everyone probably knows already, I'm not a fan of complete assimilation in which even a person's cultural identity is abandoned for the majority's. It may be BS, but it does give these people something to fall back on. It conserves their cultural origins and can enrich their present country. But in the end of the day, identify with whatever you want to identify with.