That is a very typically Mexican thing, what with the revival of indigenous pride movements starting in the 60s (interestingly, and relevantly, this movement began in the US).
In the rest of Latin America it's very common to identify as "white". When I was in Colombia, my friends told me they thought of themselves as white and even as part of the West (!).
I was also surprised by how little in common they thought themselves to have with the indigenous - considering them wholly separate despite themselves being of significant native ancestry, and despite sharing the same nation.
Other Latin American nations with "native pride" are typically far more indigenous i.e. Peru, Bolivia.
Then at the other end you have Argentina, which is stereotypically very proud of their almost-entire descent from European immigrants: "los argentinos descendemos de los barcos" as the saying goes.
Latin America is a truly fascinating place - it's just a shame that English people's sole interaction with it is through hectoring, whining Americans.
But hey, remember this: if you do choose to visit Latin America guys, there's one big advantage; no British women!