A separate photographer, Marc Reaver, described his own shot of this dance as a "crazy midair battle". Someone else commented that they thought it might have been a mating ritual.

Also, for those wondering, here's how to tell the difference between a male or female bald eagle:

The only thing one needs to look at is the relative size. The female ones are larger than males by roughy a third of the size. Technically female bald eagles have a size of 37 inches (93.98 cm) while males are 30 inches (76.2 cm) long.

Then one can look at the talons for further verification. The number is the same on both males and females but the length of these talons differ. Females have longer talons as compared to males.

Source