The company has been caught in a political firestorm because of the city's pro-democracy protests that have angered Beijing. Its business and stock price is also hurting - hundreds of its flights were canceled when protesters overran the airport and bookings are down.
"This is a grave and critical time for our airlines. There is no doubt that our reputation and brand are under immense pressure and this pressure has been building for some weeks, particularly in the all-important market of mainland China," Hogg wrote in a memo to staff which Cathay shared with CNN Business. "Could we have managed things differently? In hindsight, 'yes'."
"Recent events have called into question Cathay Pacific's commitment to flight safety and security and put our reputation and brand under pressure," said Cathay Chairman John Slosar in a statement. "This is regrettable as we have always made safety and security our highest priority."
Slosar did not elaborate further, but the airline has been swept up in numerous controversies related to the demonstrations.
China said last week that it would not allow Cathay flights crewed by people who have taken part in "illegal demonstrations, protests and violent attacks" to use its airspace, a rule the airline said it would follow.
The company source said one of the pilots was charged with rioting in Hong Kong and had been suspended from duty since July 30.
The airline was forced to cancel more than 150 flights last week amid a day of mass demonstrations and strikes. The protests at Hong Kong's international airport earlier this week led to nearly 1,000 flights being canceled.
Cathay said last week that protests affected its passenger numbers last month, and were continuing to "adversely impact" future bookings.
Cathay's (CPCAY) stock has plummeted nearly 24% since April.
"It has been my honour to lead the Cathay Pacific Group over the last three years," Hogg said in a statement. "I am confident in the future of Hong Kong as the key aviation hub in Asia. However, these have been challenging weeks for the airline and it is right that Paul and I take responsibility as leaders of the company."
Hogg will be replaced as CEO by Augustus Tang, the chief executive of Hong Kong Aircraft Engineering Company, another Swire firm. Loo will be replaced by Ronald Lam, the head of HK Express, a Cathay subsidiary.
CNN's Laura He, Michelle Toh and Sandi Sidhu contributed to this report.