Of course, there are a million ways to answer that question. You could look at available seat miles, revenue passenger miles, number of flights, number of planes, etc. In most metrics, American is still the largest US airline, but if you look at total number of passengers, Southwest has now become the largest.
In August, Southwest carried 8.7m passengers. That passed American, with 8.5m, for the first time. Surprised? You shouldn’t be. Southwest has continued to grow at a healthy pace while other large airlines have stagnated or shrunk since 2001.