For nearly six months, the mayor of New York City did not meet with the man responsible for fixing his city’s failing subway. In fact, Mayor Bill de Blasio had not even spoken with Andy Byford, the subway’s leader, since Mr. Byford arrived in New York in January.

On Tuesday, the two finally met at City Hall.

It might seem odd that Mr. de Blasio did not call Mr. Byford the first time the subway melted down on his watch or the dozens of times since then that the system unraveled, leaving many of its nearly six million daily riders stranded.

But this is New York, and the politics surrounding the subway are almost as dysfunctional as the system itself.

The fact that Mr. Byford had not heard from the mayor — revealed in a recent article in The New Yorker — was shocking to some subway riders and even to Mr. Byford himself. “Bit weird,” he said. “I should ring him up.”