What did he do wrong?
I'll go over some of the claims, from least egregious / least crazy to most egregious / craziest.
Note well: I do not ascribe to these crazy views.
Claim: Dr. Fauci lied about the efficacy of masks at the start of the pandemic and then switched lies to how efficacious masks were.
There might be something to this claim as masks were in very short supply at the onset of the pandemic and the medical community wanted to have first responders getting first dibs to that short supply.
Claim: The US funded one of the organizations that were involved in researching corona viruses at the Wuhan institute, that Dr. Fauci knew about this funding, and covered it up.
This is partly true. The US funds lots of medical research done outside of the US, and one of them did work with the Wuhan institute.
Claim: Dr. Fauci lied about the nature of the disease. It was instead a variant of the common cold.
It is true that some of the many viruses that cause the common cold are corona viruses. It is not true that COVID-19 is only as harmful as are typical common cold viruses. The best way to tell a lie is to tell a partial truth. Dr. Fauci did not lie about the terrible nature of COVID-19..
Claim: Dr. Fauci lied about the origin of COVID-19 (version 1). He knew that COVID-19 originated as a lab leak in Wuhan and Dr. Fauci hid this knowledge.
We do not know if COVID-19 originated from a lab leak or some other mechanism such as a cross-species infection that crossed to humanity at a Wuhan market. (Natural origin and cross-species infection is widely regarded as the most likely explanation.)
Claim: Dr. Fauci lied about the origin of COVID-19 (version 2). He knew that China intentionally released the virus responsible for COVID-19 virus as a biological weapon. As in version 1 of this claim, Dr. Fauci knew about this and hid this knowledge.
This one is ludicrous.
Claim: Dr. Fauci lied about the origin of COVID-19 (version 3). COVID-19 was neither a lab leak nor a biological weapon released by China. It was instead a biological weapon intentionally released by the US during a trip to China. As in version 1 and version 2 of this claim, Dr. Fauci knew about this and hid this knowledge. Moreover, Hilary Clinton was directly involved in this intentional release. (Don't ask me how.)
This one is beyond ludicrous.
Claim: The COVID-19 vaccines contain micro receivers by which the federal government will control our brains, will make us accept gay marriage, will make us reject Christmas, and will make us vote for Democrats for the rest of our lives. And, of course, Dr. Fauci knew all about this.
Beyond ludicrous is not strong enough to describe this level of craziness.
Note well: I do not ascribe to the crazy views. Please don't kill the messenger. These crazy views are out there, and some members of Congress subscribe to them.
Tucker Carlson was more specific about what supposed crime Fauci should be prosecuted for (in August 2022). The main point seems to be helping create COVID and then covering up his involvement. Both would be crimes if true (which it is not).
Carlson asserted Fauci had committed “very serious crimes” and said he “apparently engineered the single most devastating event in modern American history.”
Carlson falsely claimed that Fauci knowingly lied, resulting in people being hurt:
In just the last 2 years, Fauci’s recommended treatments and preventative measures for COVID that not only didn’t work, but that he knew didn’t work. He admitted to The New York Times [NYT] that he lied about herd immunity in order to sell more vaccines
He also falsely claimed that Fauci helped create COVID, covered up the evidence, and was conspiring with a foreign government to cover up the origins of the pandemic and to "suffocate" kids:
Oh, so he knew. As your kids were suffocating during gym wearing a mask, Tony Fauci knew they didn’t work and then there’s this, maybe his most notable crime. He didn’t simply downplay and obfuscate the origins of the pandemic, apparently in conjunction with the Chinese government. No. Tony Fauci covered up evidence that he, Tony Fauci, helped create that virus in the first place.
Rand Paul would be another example of someone alleging criminal behavior. Back in July 2021, Paul referred Fauci to the DoJ for allegedly lying to congress:
Sen. Rand Paul (R-Ky.) made good on his threat to refer Anthony Fauci [...] to the Justice Department for allegedly lying to Congress about funding gain-of-function research at the Wuhan Institute of Virology.
Chip Roy has accused Fauci in March 2022 of crimes against humanity, mainly for his support of the COVID vaccine.
Regarding Musk, he specified later:
As for Fauci, he lied to Congress and funded gain-of-function research that killed millions of people.
The claim that Fauci lied about gain of function research has been rated false by The Washington Post fact checkers.
The two largest Fauci issues (that are easily proved at any rate) are
NIH funding of gain of function research at the Wuhan Institute of Virology
The National Institute of Health (which Dr. Fauci led) openly funded gain-of-function (GOF) research (where you try to engineer viruses to do new things for the purposes of study and prevention)
On October 16, 2014, the White House Office of Science and Technology Policy announced the launch of the U.S. Government (USG) gain-of-function (GOF) deliberative process to re-evaluate the potential risks and benefits associated with certain GOF experiments. During this process the USG paused the release of federal funding for GOF studies anticipated to enhance the pathogenicity or transmissibility among mammals by respiratory droplets of influenza, MERS, or SARS viruses.
Where this potentially gets messy is the large suspicion that the Wuhan Institute of Virology (which in the city where COVID-19 was first diagnosed) was actually the source of COVID-19. I'll ignore that controversy and focus on what has actually been proved.
The National Institutes of Health admitted Peter Daszak’s EcoHealth Alliance broke its reporting rules when conducting bat coronavirus research, with critics immediately contending this means the Wuhan lab collaborator had indeed been conducting gain-of-function research and NIH lied about it.
NIH principal deputy director Lawrence Tabak said in a Wednesday letter that EcoHealth provided a five-year progress report on bat coronavirus research conducted under an NIH grant, and “the limited experiment described in the final progress report” was “testing if spike proteins from naturally occurring bat coronaviruses circulating in China were capable of binding to the human ACE2 receptor in a mouse model.”
In particular, this has lead to Senator Rand Paul (R-KY) to assert that Dr. Fauci lied under oath (which is a crime). Most notable was this fiery exchange between the two, where each accused the other of lying.
From the prior link about this not being true, we see Paul refer the matter to the DOJ for investigation and/or charges
Paul requested in July that Attorney General Merrick Garland criminally investigate Fauci over Senate testimony in which he said NIH never funded gain-of-function research at the Wuhan lab. The senator told the Justice Department that contrary to Fauci’s contention, “this research, conducted at the Wuhan Institute of Virology and funded under NIAID Award R01AI110964, fits the definition of gain-of-function research.” That specific award was the subject of NIH’s new admission.
While there are disagreements about what constitutes GOF research, it's clear the NIH was funding partners who funded some sort of research at WIV. There's no way to prove, definitively, that COVID-19 originated at WIV, let alone that this research was what created COVID-19.
Dr. Fauci admitted he tailored advice based on politics
This quote from Fauci himself, in particular, sticks in the craw of some people. From Axios
When polls said only about half of all Americans would take a vaccine, I was saying herd immunity would take 70 to 75 percent ... Then, when newer surveys said 60 percent or more would take it, I thought, "I can nudge this up a bit," so I went to 80, 85. We need to have some humility here .... We really don’t know what the real number is. I think the real range is somewhere between 70 to 90 percent. But, I'm not going to say 90 percent.
Remember, Fauci was a major voice in calling for government intervention in the COVID-19 policies that were (and in some cases still are) enacted. Admitting that you're basing such advice largely on politics, and not science, means that any government mandate (masks, vaccines, lockdowns, etc.) can be considered as political as well (regardless of any underlying science). Fauci was not alone in playing politics with COVID-19 restrictions, but he was supposed to be beyond politics and was not.
Other answers make good points but are missing the number one grievance most widely alleged against Dr. Fauci and the CDC.
That he overstated the COVID death rate. By attributing any death of a person who was COVID positive to being from COVID even if they died in unrelated circumstances (e.g. car crash). So “the death rate doesn't justify the measures taken to combat the virus's spread” https://www.usatoday.com/story/news/factcheck/2020/06/05/fact-check-cdc-estimates-covid-19-death-rate-0-26/5269331002/
They belive "that only 6% of COVID-19-related deaths recorded actually died from Covid”.. “The remaining 94% of cases were instances of comorbidity” https://www.reuters.com/article/uk-factcheck-94-percent-covid-among-caus-idUSKBN25U2IO
They (people who oppose Dr. Fauci) see overstatement of case fatality rate causing unnecessary locks downs, economic harm, mental health issues, preventing people from seeing people on their deathbeds, etc
There is a fair amount of circumstantial evidence that indicates Dr. Fauci may have knowingly covered up controversial research, and prevented a full investigation of covid's origin.
Dr. Fauci's department at NIAID funded coronavirus research at WIV in 2019, in collaboration with EcoHealth. The October 2022 US Senate report on the origins of covid all but canonizes the research lab origin hypothesis (mentioning EcoHealth by name).
The research genetically engineered the coronavirus to become significantly more infectious and more deadly when introduced into a population of humanized mice, specifically through the ACE2 receptor. The last point is notable because the SARS-CoV-2 virus penetrates the human cell by binding to the ACE2 receptor with its spike protein.
The vaccine sequence was selected on 13 Jan 2020 by a collaboration between NIAID's VRC and Moderna, a few days after China released the covid virus sequence, and well before the pandemic was declared in March. This was a non trivial development, since the vaccine sequence is not a simple clone of the virus spike protein. The key piece of the vaccine sequence was the result of decades of research on RSV, MERS and HKU to manipulate the spike protein (also shared by the covid virus) to be easily recognizable by the immune system by stabilizing the pre-fusion structure using the patented 2P mutation. So, it appears quite fortuitous the pandemic vaccine was precisely anticipated by a multi-decade research project led by NIAID, and selected months before the pandemic was declared.
When multiple scientists suggested to Dr. Fauci the coronavirus was indeed genetically engineered, since novel elements had no evolutionary precedent, Dr. Fauci arranged a private telecon, giving the appearance of push back. The scientists retracted their claim in a Nature article debunking the lab origin theory, and then the lab of the lead author, Dr. Kristian Anderson, received a significant boost in funding from the NIAID.
The EcoHealth coronavirus research could be construed as dual use research, which means it could also have military applications. Fort Detrick, which used to have a bioweapons program in the 1960s, and now has a dual use research program is only an hour away from the NIH's Bethesda campus. In August 2019 the research program was shutdown after contamination leak. There is no hard evidence the two are related, but the close proximity and historical precedent does sow suspicion in the public mind.
These are all highly suspicious points, and at least merit investigation to restore public trust in Dr. Fauci and the NIH.
My opinion is that all the grievances stated aren't the real reason. Americans don't like being told what to do, and much of that stuff was invented to rationalize their resistance to the govenment's attempts to protect us. I suspect there would have been less rebellion if they educated us instead of cracking the whip.
It didn't help (for example) here in Oregon, restaurants were put out of business as "nonessential" but liquor stores and casinos remained open.
Or that Fauci failed to enthusiastically repeat every stupid thing certain high ranking officials said.
The school closings, online learning, and mask mandates have had an impact on students that is widely described as "devastating".
Fauci was pushing mask mandates as late as February of 2022.
The last thing is that a mask only protects you while you are wearing it. Unless you want to mask for your entire life, you have to stop at some point. A lot of people, including me, thought that once vaccines were widely available, the cost of continued school masking greatly outweighed the benefit.