What factors led to Texas's independence and annexation into the US?

The disagreement over slavery, the Mexican government's inability to control American settlers, and settlers' unwillingness to adapt to Mexican laws were the main factors that led to the independence and annexation of Texas.
In 1824, the newly independent nation of Mexico passed the General Colonization Law. This law made it relatively easy and straightforward for people, irrespective of national origin, to settle in Texas. The Mexican government hoped that liberal immigration and settlement policies would help civilize the far frontiers of the nation. As a result of the Mexican policy, many Americans immigrated to Texas.
Many of the American settlers brought their slaves with them into the Mexican territory, despite slavery being illegal in the country. By the mid-1830s there were as many as 5,000 slaves in Texas. Disturbed by the flouting of Mexico's laws, Mexican President Anastasio Bustamante shut down American immigration into Texas in 1830. This act, coupled with increased customs regulations angered the Americans in Texas. When a revolt against the government broke out in 1832, the Americans settlers sided with the anti-government forces and expelled the Mexican army from much of Texas.
In 1836, the American settlers, taking advantage of the relative weakness of the Mexican government and army declared independence and forced the army out of the territory entirely in what is known as the Texas Revolution.
Soon after winning independence, the provisional Texan government petitioned the United States for annexation. They were American, after all, and wanted the security and benefits of being part of the country. They also knew that being part of the United States would encourage more settlers to come to the territory. With the vast labor shortages that existed, getting more settlers was of urgent importance. Texas had also racked up enormous debts that they hoped the United States government could pay off. The Texan government also immediately legalized slavery. Meanwhile, Mexico continued its claims to the territory.
The United States did not annex Texas until 1845. In fact, Congress only just barely approved the annexation. The delay and hesitancy to bring Texas into the United States lay partially in the fact that Mexico threatened that this would lead to war. Furthermore, as a slaveholding territory, the entry of Texas into the United States would upset the delicate balance of free versus slave territory in the country. Many abolitionist congressmen were reluctant to add another slave state to the country. There were even plans in place to divide Texas into two states, one with slaves and one without. In the end, though, the matter was put to a simple majority vote which passed the Senate twenty-seven to twenty-five.
http://www.pbs.org/weta/thewest/resources/archives/two/texannex.htm

https://avalon.law.yale.edu/subject_menus/texmenu.asp