For instance, perhaps 59% of white parents had kids who moved up, while 43% of white parents had kids who moved down.
This doesn't excuse the reporting, but it might explain it.
Perhaps it should have been written:
25% of black kids [who] had parents [that] grew up in the bottom two levels [] moved up at least one [but] 59% of [such] white kids moved up.
78% of black kids [who] had parents [that] grew up in the top three levels [] moved down at least one [but] 43% of [such] white kids moved down.
But I agree it's unclear and this is just speculation.
For instance, perhaps 59% of white parents had kids who moved up, while 43% of white parents had kids who moved down.
This doesn't excuse the reporting, but it might explain it.