​ There's more room for discussion, but you may find this earlier fine answer by /u/dhmontgomery on the topic interesting. It details how Spanish became the dominant language in Mexico through reforms in the late 18th c. and especially following independence.

A few points I'd add specifically for your question:

• It's always tricky to compare colonies that developed very differently. In many former colonies the colonizers' language is spoken, but various native languages are retained, as in India. Even between Latin American countries it's not as easy as Spanish becoming dominant in the same way: some countries like Guatemala and Peru still have high percentages of native language speakers of up to 40%.

• Still, we can note some broad structural differences between your two examples. Colonial expansionism in India of course comes much later than in Mexico. The British tended to mix much less with local populations than the Spanish - in South Asia this meant broadly a class of British officials largely apart from the native Indians. While in colonial Mexico the Spanish also stayed at the top of the social hierarchy, intermixing (either forced or for strategical reasons) played an important role from the start. This also meant increasing linguistic influence and exchange almost from the start. In addition, in India the British started imposing Christianity only very gradually; while the Spanish expansion was built on mass scale conversion to Catholicism tied to Spanish. Such structural differences should be seen as the background to concrete political measures like those detailed in the above post. (Edit: I've talked about more differences between colonial powers in this answer, with a focus on Spanish America.)

• Looking toward current Mexico: while Spanish is by far the majority language it's not defined as an official language. There are ca. 6 million speakers of indigenous languages in Mexico today connected to rich heritages. This is the 2nd largest group in Latin America, though small percentage wise compared to other countries like those mentioned above. Nahuatl has the highest number with over a million speakers, followed by Yucatec Maya and a wide variety of other languages. Here we can note an official discourse by the Mexican government of promoting indigenous cultures languages which is not necessarily followed through in reality (to put it mildly).

• Bringing all this back to colonial times now. The focus of the Spaniards on the imperial languages of the Aztecs (Nahuatl) and the Incas (Quechua) meant that these actually replaced other indigenous languages - e.g. due to their use in official and religious contexts. At the same time, I know for Nahuatl that it gradually adopted Spanish influence. While this meant only certain Spanish words during the 16th c., by the mid 17th c. there was already stronger structural Spanish influence on Nahuatl. So we can keep in mind here colonial influences until today through a) the Spanish focus on indigenous lingua franca, and b) also limited Spanish linguistic influence on these.

​ (Edit:) Since demography has come up in the questions - the indigenous demographic catastrophe in Spanish America was very real. Numbers vary sometimes widely between regions, but we do have good studies for Mexico where roughly 90% of the indigenous population died over the first 100 years after European contact. This came through major epidemics to which there was no immunity, the combined effects of warfare and forced labor and resettlements among others - these would in turn create the conditions for further epidemics. By the mid 1700s the native population was finally slowly starting to grow again.

Yet, throughout the colonial period indigenous people were in the majority in Mexico, with a growing group of Africans and mixed descendants (ca. 40% by the mid 17th c.), and a very small group of Spaniards at the top of the social hierarchy. Plus until the 18th century at least the Spanish Crown recognised native language documents in colonial courts, and thought those languages helpful for Christianisation, a cornerstone of their rule. So that Spanish did not spread only due to the catastrophic death rate of native people - although this surely effected it. The forced language changes had more to do with intermixing between all those groups, as well as changing colonial policies that increasingly marginalized native languages, as mentioned above.

I dispute your premise that most colonised nations retain their native languages.

Take English, as spoken in England. The language derives from Germanic tribes who colonised England in the 5th century (the very name of which came from the Angles, which was in turn named after the Anglia peninsula in modern day Germany).

Of course it’s modern form owes enormous influences to Norman French which came from the Norman colonisation of England (the one in England, not the peninsula in Germany) during the 11th century.

Of course the spread of English to other colonial possessions (such as US, Canada, Australia) and close neighbours (Ireland) is well known but its spread goes way beyond that: 95% of people in Philippines speak English (making it the 3rd largest English speaking nation globally). India is 2nd (125 million people), Nigeria 4th. The UK itself comes 5th, ironically only one place ahead of Germany where 45 million people speak English (56%).

English is of course a remarkable outlier, but it’s replicated elsewhere: there are 13 countries where >50% of the population speaks French.

With regard to India itself, one unique consideration is that it is a continent sized population speaking many different languages even today. Even today only 57% of the population speaks Hindi (the #1 language) and English is the #2 most spoken language ahead of Bengali, Tamil, Urdu, Gujarati, etc.

This isn’t specifically about Mexico but you see the same thing in Ireland, When a colonizer comes into an area with a decentralized (or even multiple) governments and actively seeks to essentially eradicate the native language(s) it often happens. In the case of Ireland it was a protracted effort that existed for most of its colonial rule, school children would be beaten with sticks of caught speaking Gaeilge (Irish) in school etc.

There’s a very good, primary source, description of this language change presented in “Juan Dominguez de Mendoza: Soldier and Frontiersmen of the Spanish Southwest”. It was published in 2012 by the University of New Mexico Press.

Anyhow, the official language for Spanish Mexico was a variation of Spanish called Castilian. It was predominantly present in Spain and the more elite classes of society in Mexico.

The variation of the Mexican language today is more closely associated with the lingo of the lower classes of Spanish society back then. It was a common vocabulary that most of the native Mexicans spoke during their war of independence against Spain in the mid-1800s.

Most of India didn't retain their native languages after Mughal rule (17th century). The language that we call Hindi cannot be considered India's native language because it developed by the amalgamation of Persian and existing Indian languages (Brijbhasha and Khariboli) during the 17th century. Hindi is the most commonly spoken language in India.

This is complicated by the fact that there are dozens of major regional languages and dialects in India that weren't affected by Western/Persian Imperialism. Also, during the British rule (19th century), English didn't end up replacing Hindi, but it found widespread usage as the language of the elites, a status that it still retains today.

I've commented on this with references before.

Lots of mezzo americans died because of diseases the spaniards brought with them. Their numbers dwindled so much that the numbers of the spanish colonists numbers were something to contend with. Meanwhile there was no disease the brits brought to india that greatly diminished their numbers and the brits sent far less colonists to india.

Because India retained it's indigenous (pre-colonial) population, while the natives of Mexico were wiped out by disease. There are no (or very few) full blooded Aztecs, Mayans, etc. in Mexico today, only people of mixed ancestry.

Very few elements of Aztec/Mayan culture were preserved, most of it was destroyed by the Conquistadors.

Also India is a pretty ancient civilization, far older than any European country. They made many accomplishments that impacted the world prior to colonization. The whole old world knew of India and the Hindi language. It'd be very hard to wipe away all that written history. The Aztecs were fairly new to the scene, plus very few peeps went to the new world. The ones that did either didn't stay, or didn't come back to tell the story (yes, Mansa Abubakari II, I'm looking at you)

I can't say for sure about the Mayans though, somebody Google that.