Edit: I'm never sure if I should post or not, but this one is close to my heart and a topic I've studied.

I'm no historian, but this is a topic of interest to me and I've done a lot of research on it. The secession of Texas from Mexico is a complex subject, many factors played in to it and I could write volumes on it. I'll answer your question as best I can and provide a strong alternative point of view.

Slavery was a factor, but perhaps your history teacher overstated his case. Vincente Guerrero, who was the second President of Mexico banned it via the Guerrero Decree in 1829 and that did raise tensions with the white settlers. However, in December of that year Agustin Viesca, former governor of Coahuila and Texas and current Secretary of Relations for the Guerrero government wrote that nothing would change in regards to slavery in Texas.

A huge factor was the implementation of Las Siete Leyes by Santa Ana in 1835 which federalized the Mexican government to a large extent and a generated a desire by the residents to return to the 1824 Constitution which granted more independence to the states.

I referred to the following sources for the quick summary, knowing what to Google helps a lot. You can find more complete answers in them, or if the mods will allow this to stay up, I'm happy to post more. The 1824 Constitution and Las Siete Leyes can be found on Wiki, even they can't mess up actual historical documents.

http://www2.austincc.edu/lpatrick/his1693/causes.html https://tshaonline.org/handbook/online/articles/ngg01