The primary reason why the Republic of Texas had trouble joining the United States was due to the opposition from Northern congressmen who were against the expansion of slavery. Many Northern leaders were concerned that admitting Texas as a state would add another slave state to the Union, which would further tip the balance of power in favor of slaveholding states in Congress.
Additionally, there were concerns about the implications of annexation on U.S.-Mexico relations, as Mexico still considered Texas to be a part of its territory following the Texas Revolution. There were complexities surrounding the idea of Manifest Destiny as well, but the main impediment was indeed the debate over slavery and its expansion into new territories.
In summary, the most fitting reason is: because Northern congressmen who were against slavery did not want another slave state.