[Between the Lines]

The idea, as I had it explained to me, is that by blending the European race with the Mesoamerican, Mexico has brought forth a new race, the mestizo or bronze race, which is claimed to be superior to both the contributing races, I suppose by dint of hybrid vigor.

La Raza actually refers to what they believe is a new race of people made up of all of the old races of the world called La Raza Cósmica (the cosmic race) which will eventually absorb all of the old races and create a new worldwide civilization called Universópolis.

In the same way that La Raza claims Atzlan because they are descended from the Aztecs, they can also claim the rest of the world being as they believe this new race is descended from all races. Atzlan isn't the ultimate goal, it is just the beginning.

[quadrant]

The people that explained this theory to you seem to have a poor grasp of reality and history.
The idea that current Mexicans are descended from the Aztecs is absurd. Most of the inhabitants of Mexico before Cortez were not Aztecs. In fact, the majority of the population was oppressed by the Aztecs.
As to the prediction that a news race of people will be born, one wonders if the proponents of Aztlan have consulted the Chinese on this matter. And if a new race of people is going to be born, why would they want to use Spanish as their language?