The Southwest U.S. was never part of Mexico. It was under control of Spain for a short time, though.
A common misconception.
Sorry, I meant to say it wasn’t settled by Mexico, it was settled by the Spanish Conquistadors, the Church and Spanish Citizens via Spanish Land Grants. It did however come under Mexican rule with Mexico’s independence from Spain. Throughout most of history it was not part of Mexico. Mexico did little for the area and the settlers were left to fend for themselves while under the Mexicans.