Why do most hurricanes in the US occur in late summer or early in the fall?

Because this is when the ocean's waters are the warmest. Recall that the summer solstice is around June 21 (using the northern hemisphere for this example), which is when the suns rays are strongest in the northern hemisphere. It typically takes another month or so for most areas to experience, climatologically, their warmest summer weather. This is because it takes time for the land to heat up and air masses to move poleward. But water takes longer to heat up than land, and it is not until later in August and September that water is at its warmest (consider that Arctic sea ice reaches its minimum in mid-September, which is nearing the equinox)!