Because the CDC is consulting with the people who have been doing the Ebola research and going to Africa to contain outbreaks for the last 40 years. Plus, the CDC is familiar with the entire body of literature written by those same researchers and health care workers.
Being very familiar with the research myself, it's easy enough for me to verify what the CDC (or anyone else) says. So far, the CDC has been accurate--armchair pundits, not so much.
To evaluate CDC statements, you must see both the science and the politics, and be able to distinguish the relative role of each.
Surely you’ve heard the accusation that the CDC is mostly working to control information, while neglecting the control of disease.
The accusation is correct.