Big is related to Sale. Sale is related to Special. Special is the opposite of Average. Average is a different concept from Bad. 
Dad is related to Male. Male is the opposite of Woman. 
Big <--RelatedTo--> Sale <--RelatedTo--> Special <--Antonym--> Average <--DistinctFrom--> Bad 
Dad <--RelatedTo--> Male <--Antonym--> Woman 