American cotton farmers and cattle ranchers felt crowded as the population grew and cheap real estate became hard to find.
They saw a promised land in the wide open spaces of Texas.
As for Mexico, it did not so much desire Americans as it feared Europeans. Because Texas was thinly populated, Mexico worried that Britain or France would try to take it away, unless settlers could be found.
By 1830, more than 20,000 Americans were in Texas, outnumbering Mexicans by more than three to one. At this point, Mexico began to regret its liberal immigration policy. Texan Americans mostly governed themselves and ignored Mexican law.
As the United States made offers to buy Texas, Mexico became worried about losing the state.