McCarthy is, bizarrely, trying to tack left -- promising to reverse school closings by redistributing funding away from the North Side, showing up at the March for Our Lives, talking about creating a more progressive tax structure.
He knows the north side is Rahm's base, but there's enough voters in the rest of the city to overpower them.
What's bizarre is that northsiders (in Illinois, we don't use the term "limousine liberal", instead preferring "lakefront liberal") are easily the most liberal voters in the whole city. The remainder of Chicago doesn't care about having a progressive tax or gun control. I guess they do care about losing all those schools, though.