Because they are living and working in an area of outbreak, in close contact with victims AND ASSYMPTOMATIC CARRIERS.
Typically people don’t go to the doctor until they feel ill. At this point with ebola the patient is already infectious. Medical personnel would have to wear protective clothing to see every patient, changing it each time a new one is seen.
Because the virus can survive on surfaces for hours, if not days, the possibility of infection exists without even seeing the infected person.
Is this aspect being downplayed? You betcha.
Why?
Economics.
Panic avoidance: Most of the people who have contracted the virus had physical contact with someone infected or contaminated materials, commonly in a clinical or family setting.
It is not well documented how little contact with infected people or contaminated surfaces is sufficient to transmit the disease, because greater levels of contact have been either documented or assumed.
Many medical supplies Americans would simply discard in biohazard bags to be burned are washed and re-used there, because they are in short supply.
While clinicians, once aware of the possibility of Ebola in the US might be better prepared and equipped to remain uninfected, this is a level 4 biohazard--worthy of the 'space suit-independant air supply' regimen.
If it pops up in the ER somewhere, there is a solid chance someone will get infected, and by the time the risk is realized, they may have passed it on (incubation takes from 2 to 21 days, depending on the individual and the initial viral load).
We haven't even started to go into the possibility of infection from contaminated surfaces, but the possibilities are almost unimaginable in an environment where there are points of common contact virtually everywhere--from handrails to door knobs, counters, ATM keypads, gas pumps, etc...
The trace smear of blood or sweat on any surface might be enough to kill you, because as clean and germ conscious as we think we are, people have become lax about hygiene. Touch the counter, rub your eye, and you could be infected--that dangerous.
Now imagine the effect of people realizing that on shopping, dining out, public transportation, and you begin to get the possible effects, not only on the population, but the economic spasms which could accompany an outbreak.
ASSYMPTOMATIC CARRIERS and a possible airborne mutation. Simple answer is we don’t know a lot about Ebola other than it is highly contagious and has high mortality. If we look at historic pandemics like the Spanish influenza after WW-I and the Black Death we are only learning years later about how these diseases may have spread. During the time of the plague there was an apparent pneumonic disease with even higher mortality than the plague. The disease referred to as the English sweating sickness killed within hours of symptoms appearing..mainly high fever and profuse sweating. The cause of this pandemic is still unknown.
... and those carriers with symptoms have only symptoms like diarrhea & vomiting - which are found in many very common and non-serious health problems (and even in people with no health problem).
Therefore you can't quarantine everyone who has Ebola like symptoms and can't separate the symptomatic who have Ebola from those who don't until they already had the opportunity to spread the disease.