Mexicans will seek all kinds of excuses to justify why are they illegally pouring into the U.S. in hundreds of thousands a year through America's porous border.
They will claim that American Southwest is their "historic land", although when Mexicans signed in 1848 a treaty with the U.S. in which they ceded their claims to these territories, out of est. 4,000,000 people (mostly, North American Indians) living in there, only est. 4,000 residents in California, Arizona, Nevada, Utah, Wyoming, Colorado and New Mexico were Spanish speakers, and a vast majority of them Spaniards and not Mexicans. (The highest published claim I saw was "no more than about 7,500 Spanish speakers" in California itself - see  - out of a total of about 300,000 California residents.) Compare this to Mexico's population of about 7,500,000 at that time to conclude that less than one in thousand Mexicans lived in the American Southwest at the time when the treaty was signed.
They will claim that they have rights to American territories because they are indigenous people here, kins of North American Indians and California Indians, although the main premise of this kinship is Christopher Columbus's famous mistake: when he discovered America in 1492, he thought that he landed in India and named all the people that lived there "Indians". If this kinship by name ("Indians") were a valid argument, it would give Mexicans territorial rights against India because of their Indian descend.
They will claim that they are only coming to America to do jobs that Americans won't. But if you look at American job market, Mexicans are expanding their presence there to the point where they monopolized entire sectors of economy in which they managed to drive American workers away by depressing the wages prevailing in these sectors. This monopolization begun with picking strawberries, but then it carried on to landscaping, gardening and housekeeping, then to construction, then to food and hotel industries, and on and on and on. In the sectors where they are still "underrepresented", they demand quota for new hires on their behalf, although in other sectors where they have a practical monopoly there are no quotas for underrepresented (and displaced) American workers.
They will claim that they had to leave Mexico in order to improve their lives, but the fact is that as living standards in Mexico (slowly) improve, the number of "migrants" is growing rather than decreasing. Once in the U.S., although their lives have been dramatically improved, they apply even more pressure to increase Mexican population in the U.S. up to the point where American births to Mexican parents compete with mass "migration" for the lion share of this country's population growth. So, although they blame their economic understatus in Mexico for growth of their population in America, the fact is that every improvement of that status immediately translates on visible increase of their population.
Their "Mexican historicity" and ethnicity-based claims don't withstand scientific scrutiny, though. The native peoples living in Americas, although arguably all descendants of Mongolian nomads that found their way through Bering's Strait to American continent some nine millennia ago, are about as ethnically diversified as peoples in Europe are today. (No one in Europe would suggest that the Portuguese have any territorial rights to Finland just because they are indigenous European people.) There were no social or cultural structures in place that would made of Americas' inhabitants one people. They had different cultures and languages, and fiercely fought with one another. There was not enough trade or cultural interaction to foster any close ties between them. In particular, there was no meaningful "kinship" between North American Indians and native residents of Mexico.
For example, the areas of San Fernando, San Gabriel, San Buenaventura, and San Bernardino, situated right at the center of what Chicano activists call their "historic land", were populated by Yuhaviatam Nation of Shoshone Indians that Spaniards nicknamed "Mission Indians". These Indians had about as much in common with Mexicans as other North American Indians had, that is, nothing, except for their ancient Mongolian ancestry....
We need to recognize that the root cause of the Mexican mass "migration" to the U.S. is not their "reclaiming" of the land lost but their rapid population growth that largely exceeds that nation's ability to feed, educate, and house its population. Recognizing this gives us a valuable hint what should we do in order to bringing that "migration" to a complete halt. Rather than accepting millions of "migrants" who further perpetuate the explosive population growth, this time in the U.S., we should fully enforce the American border and make it clear to Mexican authorities that we will not accept any surplus of their population anymore. Rather then importing Mexican "temporary" workers or otherwise stimulating growth of Mexican economy, the aid that quickly translates into more population growth and, eventually, more "migration" to the U.S., we should concentrate our efforts on stabilization of the Mexican population and throw in no money there until such a stabilization has been accomplished....