The data doesn't really back this up. Like everything else, Americans view of the World Health Organization basically falls on partisan lines.
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What is your personal impression of the WHO?
Here are my impressions. Had the WHO given out a correct information early, the spread might have been contained in China, and they have been consistently wrong. It's hard to imagine how any group could be so wrong on so many aspects of it.
Next to fail was CDC. They had a full month to prepare, to ramping up testing, and to building a system of contact tracing. Trump bought them a little extra time with his one correct move, banning travel from China, which bought about 2 extra weeks. Still, the CDC was only able to conduct a handful of tests while other countries were conducting thousands. CDC effectively blocked the tests developed by others, such as the University of Washington, by requiring their tests to be validated against SARS and MERS, but refusing to ship them samples of SARS and MERS.
Next up, Trump started injecting himself into the middle of the issue, one that he wasn't qualified to handle, and making crazy pronouncements like "poof, it will vanish". The CDC continued to be wrong for awhile, for example, advising against mask, and saying the virus could not aerosolize, but in their defense, it was partly because they were getting wrong information from the WHO. Meanwhile the WHO continued to give out wrong information at every turn.
After that, however, the CDC got going and did a fine job. Their testing finally began to ramp up, and they began approving the independent tests, further ramping up testing. They adjusted their views as new facts came in, such as data on aerosolization from UNMC. They reversed on masks, and recommended that everyone wear masks.
Thus, my opinion is that the CDC failed early, when it was most critical, but since those early errors is doing well. Sadly, the WHO is still issuing crazy pronouncements, such as recently saying that asymptomatic transmission is not a problem one day, and then retracting it the next. I believe they are still saying that there is no reason for non medical workers to wear masks.
Trump could have come out of this with dominant position for the election, and become unbeatable. Leaders almost always gain high approvals in times of crisis. All they have to is lead. Trump could have called for unity, then put experts in charge, and allowed them to do their job, and followed their recommendations. Had he done so, his popularity would have soared. He would gained support if the virus turned out to be nothing, because he was Presidential, and he would have gained support if it turned out to be serious, even if the economy crumbled, because he was decisive. Instead of taking the win-win position by acting Presidential, he took took the risky route, and made a huge bet that the virus would be no big deal, and go away on it's own. It hasn't, so his approval rating has fallen.
So, my grades:
CDC: C. They are doing very well now, but their early failure was costly. Their grade would be higher but for the fact that what is done early is critically important.
Trump: F. After banning travel early, he has done very poorly
WHO: F-. How could any group be more wrong on more issues? They were wrong early. Even today I think they still recommend against masks.
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From my vantage point, the handling of Covid became political basically immediately. From the left, the blame went to Trump. And because Trump's handling was so obviously terrible and the Right couldn't figure out a reasonable way to justify it, they tried to pass the buck onto the WHO and CDC. It seems to have worked, but only amongst Republicans.
I don't see this as a buck passing issue. The failing of one group does not forgive the failing of other groups. Errors by WHO do not absolve Trump, and errors by Trump do not absolve the WHO.