The post-pandemic surge of demand for premium air travel is where large carriers are making their money, and American Airlines Group Inc. is missing out on the bonanza.

The reason is clear to Chief Executive Officer Robert Isom. The strategy to push corporate accounts to book flights directly with American Airlines has rubbed flyers the wrong way, and they are choosing competitors. The architect of that strategy was Vasu Raja, American’s charismatic chief commercial officer, whose departure was announced in a terse statement on........

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