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Ihustled up the stairs out of the F/G train station on Seventh Ave. in Park Slope, late for a doctors’ appointment, and nearly smacked into a wall of muscular men wearing earpieces. Just ahead the NYPD security detail: Mayor de Blasio, ambling down the block and shaking hands on a sunny Wednesday afternoon. The mayor made his way into the Soup Bowl, chatting up the staff and eventually emerging with some lunch. It was a charming little scene, and part of the appeal and promise of a de Blasio mayoralty — that he would be a refreshingly down-to-earth change after 12 years of AUTOCRATIC billionaire Michael Bloomberg in City Hall. Not only stylistically, but politically: Candidate de Blasio’s winning theme in 2013 was that New York had become more economically imbalanced than ever, that both incomes and opportunities were now unfairly unequal, and that he would fight hard on behalf of regular folks. But by the end of the day, the regular-guy glow I had witnessed started to wear off. The mayor did many things that Wednesday: made taped appearances on two radio stations; staged a press conference at the Brooklyn Museum to highlight plunging crime statistics; left town for Washington, D.C., to attend a campaign fundraiser the following morning at the national headquarters of a teachers’ union; and enjoyed that leisurely soup lunch He hadn’t bothered to stop at Brooklyn’s Atlantic Terminal, where a Long Island Railroad train had derailed, injuring 106 people. Gov. Cuomo had raced to the scene, along with his MTA chairman, Tom Prendergast. The city’s fire commissioner was there, too. Quizzed about his own absence from the emergency, the mayor shrugged, verbally. “The LIRR obviously is the purview of the governor,” de Blasio told reporters — eliding the likelihood that many of the banged up commuters work and pay taxes in the mayor’s jurisdiction. “But more importantly, thank God, there are minor, very minor injuries.” Everyone is in favor of injuries being minor. But de Blasio’s odd choices on that January day illustrated the paradox that has been his first term as mayor. He has largely followed through on his promise to reorient City Hall’s priorities away from New York’s elites and toward its lower-income strivers, delivering expanded pre-k, a higher minimum wage, and paid sick leave. Crime is down; jobs and graduation rates are up. But as de Blasio launches his re-election campaign, the mayor is dogged by the perception that he’s hopelessly entangled in political feuds and calculations; that he doesn’t work terribly hard; and that he’s beholden to moneyed interests. Three years in, he can still comes across as a MAN who’s got his head in the clouds, his feet less than firmly planted on the ground. Who is somehow both an unrealistic idealist and