Carrie Lam, Hong Kong’s first female leader, does not lack self-confidence. A devoted Catholic who believes she has a place in heaven because “I do good things”, she has shown equal faith in her judgment on earthly matters.

After a heavy-handed and widely criticised police crackdown on protesters this week, she provoked outrage by weeping over the sacrifices she said she had made for the city, before comparing opponents hit by a barage of teargas, rubber bullets and pepper spray to spoiled children in need of discipline.

Lam has staked her authority on the extradition bill that has brought so many people on to the streets this week. Her implacable sense of conviction – critics call it arrogance – originally helped carry her from a modest home in the crowded central district of Wan Chai to the pinnacle of power in Hong Kong. But it may leave both her and Hong Kong particularly vulnerable as the city faces one of its most serious challenges since the handover from British rule.

“She is a pretty arrogant leader. She likes to remind people that she always came first in class, if people disagree with her she tries to correct them, she likes to prove that she knows best,” said Kenneth Chan, a professor in the department of government at Hong Kong Baptist University. “She does not take opposition or dissent well. And her intransigence has caused a serious governance crisis.”

The protests were a response to her efforts to push the extradition bill through the territory’s legislature. The law is hugely unpopular, not just among democracy activists but also much of the city’s business community, because it is seen as a full-frontal assault on the judicial firewall that has separated Hong Kong from China and allowed its economy to flourish.

Critics fear that under the law anyone, from dissidents to entrepreneurs, who falls out with Chinese partners risks being sent to the mainland, where they will face trial in a notoriously opaque judicial system.

Carrie Lam speaks during a press conference at the government headquarters in Hong Kong. Photograph: Anthony Wallace/AFP/Getty Images

Lam has become a lightning rod for protesters, with many carrying signs criticising her or calling for her to step down.

Controversy around the bill has seen Lam’s support sink to a record low. Two years into her tenure, she is less popular than any of her predecessors were at the same point, according to the University of Hong Kong’s public opinion programme.

That public frustration was not inevitable, although Lam was far less popular than her main rival when she ran for chief executive in 2017, and won only because she was Beijing’s favoured candidate.

Ordinary Hong Kong residents do not get a vote on their leader. Instead, pro-Beijing interests dominate the 1,194-member committee that elected Lam.

One of five siblings, Lam excelled at school, joined the colonial civil service under British rule, then continued her rise after Hong Kong was handed over to Chinese control, under a “one country, two systems” arrangement meant to ensure a degree of autonomy.

A reputation as an effective operator helped earn Beijing’s support, and eventually the top job. In her previous role as chief secretary, effectively deputy to the territory’s leader, she had been nicknamed “the nanny”, in a misogynist tribute to her role clearing up the messes of other officials.

From the start of her tenure, she has struggled to bat away accusations that she answers more to Beijing than Hong Kongers.

She alarmed many last year when she named China’s president, Xi Jinping, as the leader she most admired. China’s most authoritarian and powerful leader since Mao Zedong has presided over a harsh crackdown on civil society, the reintroduction of mass internment camps in western Xinjiang, and a cult of personality.

Lam told the Financial Times: “I find President Xi more and more charismatic and admirable in the things that he is doing and saying.” However, she insists she is politically independent.

“To say that I am just a puppet, that I won this election because of pro-Beijing forces, is a failure to acknowledge what I have done in Hong Kong over the last 36 years,” she told the BBC after a campaign in which she tried to emphasise consensus.

That message, with the slogan “we connect”, initially won her some leeway. “People were willing to give her the benefit of doubt, she had pretty good approval ratings at the start of her term,” said Chan.

But that support has long vanished. As the protests gather momentum, the woman who once said God called on her to run Hong Kong may now be praying for a way out of the crisis she brought upon herself and the city.