Chrysanthemums ( ), sometimes called mums or chrysanths, are flowering plants of the genus Chrysanthemum in the family Asteraceae. They are native to Asia and northeastern Europe. Most species originate from East Asia and the center of diversity is in China. There are countless horticultural varieties and cultivars.
Chrysanthemums are flowering plants which are classified as part of the Asteraceae genus and the Chrysanthemum family. 
The context writes that Chrysanthemums are part of the genus Chrysanthemum and the family Asteraceae, not the other way around. The system might not have been able to detect that the proper names for the Chrysanthemum's genus and family had been swapped.