Many Americans believed that Texas belong to the United States. They thought Mexicans or Native Americans in between the expansion in the united states from the Atlantic to the pacific should be kicked out to make way for the "rightful" owners."
A constitution was written by mexico when american settlers were arriving in Texas and Texans had great freedom to rule themselves. But later a new constitution came which gave the Mexican government more control, which outraged many Texans.
Slavery was illegal in mexico, but most of american settlers were from the Southern states where slavery was allowed and some american's brought there slaves with them. But because slavery was illegal in Mexico, many settlers were afraid the Mexicans would not let them keep their slaves.