There are two main reasons why O’Sullivan would have wanted to deny that the annexation of Texas had anything to do with slavery.
First, O’Sullivan wanted everyone in the country to agree with him on the idea that it was America’s “manifest destiny” to expand. He did not want expansion to be something that only appealed to the North or to the South. If he had argued that expansion and slavery were closely connected, he might have upset people in the North. They might have been reluctant to support expansion if slavery was its goal.
Second, O’Sullivan wanted the idea of manifest destiny to sound noble. He did not want to make it seem that the United States was expanding for selfish reasons or for some sort of ignoble reason like acquiring more land for slavery. He wanted it to seem that the US was expanding because God wanted it to and because its expansion would be a benefit to the entire world.
Thus, O’Sullivan wanted to leave slavery out of the discussion because he wanted broad support in the US for his ideas and because he wanted US expansion to seem noble and beneficial to mankind.