As revolts go, the Texas Revolution was remarkably short, and unusually successful. The simple matter is that the predominantly American-born Texians (the English speakers north of the Rio Grande) wanted their independence from Mexico, and so they took it. The Mexican republic, based in Mexico City, was not in any sort of condition to stop it, despite their remarkable victory over Spain in 1821.
So on 2 October 1835 the Texians declared Texas independence. Their issue was that the increasingly autocratic government of President Antonio López de Santa Anna had essentially cancelled the 1824 constitution, and had tried to emulate the draconic noble rule of Spain, without a titled nobility. Further, it was slaves. Texas allowed them; Mexico did not. In theory Mexico could enforce the prohibition, but for practical and pragmatic reasons (slaveowners were paying more in taxes and raising more in revenue) they did not.
It wasn’t until February 1836 when Santa Anna personally led an army into Texas, murdering all the way. On 2 March 1836, the Texas Convention declared Texas to be independent, again. The next day, another thousand Mexican troops arrived at San Antonio de Bexar, closing up the siege of some 180 men and at least 50 women and children at the old Alamo mission. Under these conditions, “independence” was a theory, not a fact, as any rebel knows.