It's important to note that China had some evidence of human-to-human transmission as early as December 2019
The symptom onset date of the first patient identified was Dec 1, 2019. None of his family members developed fever or any respiratory symptoms. No epidemiological link was found between the first patient and later cases. The first fatal case, who had continuous exposure to the market, was admitted to hospital because of a 7-day history of fever, cough, and dyspnoea. 5 days after illness onset, his wife, a 53-year-old woman who had no known history of exposure to the market, also presented with pneumonia and was hospitalised in the isolation ward.
By late December, that evidence had grown considerably
The majority of the earliest cases included reported exposure to the Huanan Seafood Wholesale Market, but there was an exponential increase in the number of nonlinked cases beginning in late December.
While the WHO timeline might want to claim credit for noting that as early as Jan 14, that is contradicted by the WHO public statement it made that same day (as noted in the question). That same day Wuhan reiterated they did not believe COVID-19 was spreading from human to human (Google Translate below)
- As of now, have you found any cases of person-to-person transmission?
Existing findings indicate that there is no clear evidence of person-to-person transmission, and the possibility of limited person-to-person transmission cannot be ruled out, but the risk of continuing person-to-person transmission is low. At present, further research is being conducted in combination with clinical and epidemiological data.
It wasn't Jan 19, either, when the BBC has this quote from the WHO
Chinese officials say there have been no cases of the virus spreading from one person to another.
Instead, they say, the virus has crossed the species barrier and come from infected animals at a seafood and wildlife market in Wuhan.
The WHO's China office said the analysis was helpful and would help officials plan the response to the outbreak.
"Not enough is known to draw definitive conclusions about how it is transmitted, the clinical features of the disease, the extent to which it has spread, or its source, which remains unknown."
The first public WHO statement indicating human-to-human transmission came on Jan 22
Data collected through detailed epidemiological investigation and through the deployment of the new test kit nationally suggests that human-to-human transmission is taking place in Wuhan. More analysis of the epidemiological data is needed to understand the full extent of human-to-human transmission.
The WHO did not act like it believed its own reports
Just saying Jan 22 doesn't really explain why the linked stories are so critical.
Despite the fact that its own investigations were showing human-to-human transmission, the head of the WHO continued to criticize countries limiting or banning travel to China (article is dated Feb 03, but unclear what date the quotes come from)
WHO chief Tedros Adhanom Ghebreyesus says 151 cases of the disease and one death have been confirmed in 23 countries outside China. He says this small number of cases can be managed without countries resorting to extreme measures.
"There is no reason for measures that unnecessarily interfere with international travel and trade. We call on all countries to implement decisions that are evidence-based and consistent. WHO stands ready to provide advice to any country that is considering which measures to take,” Tedros said.
The WHO head then later praised China for limiting the outbreak (WHO speech from Feb 15)
We are encouraged that the steps China has taken to contain the outbreak at its source appear to have bought the world time, even though those steps have come at greater cost to China itself. But it’s slowing the spread to the rest of the world.
We’re encouraged that outside China, we have not yet seen widespread community transmission.
The WHO would finally declare a pandemic on Mar 11, long after COVID-19 had exploded worldwide
In the past two weeks, the number of cases of COVID-19 outside China has increased 13-fold, and the number of affected countries has tripled.
There are now more than 118,000 cases in 114 countries, and 4,291 people have lost their lives.
It contains these statements seemed more interested in blunting criticism
WHO has been assessing this outbreak around the clock and we are deeply concerned both by the alarming levels of spread and severity, and by the alarming levels of inaction.
And we have called every day for countries to take urgent and aggressive action.
We have rung the alarm bell loud and clear.
For some people, the conclusion they draw is that the WHO did not believe it was a seriously contagious disease until Mar 11, when the disease had already shut down most of the world.