Why were the Navajo forbidden to speak their own language in government schools?

Answer 1

This misguided and destructive policy was not only for Navajo but was in place on all government run Indian school and those run by religious institutions. It happened to native Hawaiians too. Starting in the 1868, Indian Peace Commission made a number of recommendations on how to subjugate Western tribes. It concluded:
"In the difference of language today lies two-thirds of our trouble.... Schools should be established which children would be required to attend; their barbarous dialects would be blotted out and the English language substituted. ... Through sameness of language is produced sameness of sentiment, and thought; customs and habits are moulded and assimilated in the same way"
At first, some missionary schools objected as they had been developing bilingual curriculum and traditions but soon it became the norm across Indian lands. Carlisle Indian school which started in 1879 was seen as a model. Kids from many different tribes were forced to go there. The slogan was: “Kill the Indian: Save the Manâ€.
Many, even well meaning, people believed this sort of thing. They thought, mistakenly, that Native Americans were a vanishing race whose only hope for survival was rapid cultural transformation. they thought this was best. This included some native people. Other native people resisted and hide some or all of their children. The Hopi, right next to the Navajo, were sent to Alcatraz prison for not sending their kids to such a school. 19 men spent a year there in 1894-95. For the Navjo many places were so remote from roads and authorities that some children could be hidden. But many others wanted the advantages of education for their kids and these policies came with that.
A good description of this is in Chester Nez's (1921 – June 4, 2014) memoir called Code Talker. He describes the various teachers attitudes when he arrived at school not speaking English. Ironically of course his ability to retain his language made him and others very valuable in creating a unbreakable code using Navajo as a starting place. Strangely, he says the harshest teachers were Native people of other tribes who had gone through the system to become teachers. They truly must have thought they were helping the kids. Other teachers and authorities were clearly of a sadistic and punitive mindset.